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2,290 results on '"GOMES, A. A. M."'

1. Enumerating minimal dominating sets and variants in chordal bipartite graphs

Author

Castelo, Emanuel, Defrain, Oscar, and Gomes, Guilherme C. M.

Subjects
Computer Science - Data Structures and Algorithms, Computer Science - Discrete Mathematics, Mathematics - Combinatorics
Abstract

Enumerating minimal dominating sets with polynomial delay in bipartite graphs is a long-standing open problem. To date, even the subcase of chordal bipartite graphs is open, with the best known algorithm due to Golovach, Heggernes, Kant\'e, Kratsch, Saether, and Villanger running in incremental-polynomial time. We improve on this result by providing a polynomial delay and space algorithm enumerating minimal dominating sets in chordal bipartite graphs. Additionally, we show that the total and connected variants admit polynomial and incremental-polynomial delay algorithms, respectively, within the same class. This provides an alternative proof of a result by Golovach et al. for total dominating sets, and answers an open question for the connected variant. Finally, we give evidence that the techniques used in this paper cannot be generalized to bipartite graphs for (total) minimal dominating sets, unless P = NP, and show that enumerating minimal connected dominating sets in bipartite graphs is harder than enumerating minimal transversals in general hypergraphs., Comment: 22 pages, 2 figures

Published
2025

2. Self-assembling of Ge quantum dots in an alumina matrix

Author

Buljan, M., Pinto, S. R. C., Rolo, A. G., Martín-Sánchez, J., Gomes, M. J. M., Grenzer, J., Mücklich, A., Bernstorff, S., and Holý, V.

Subjects
Condensed Matter - Materials Science
Abstract

In this work we report on a self-assembled growth of a Ge quantum dot lattice in a single 600-nm-thick Ge+Al2O3 layer during magnetron sputtering deposition of a Ge+Al2O3 mixture at an elevated substrate temperature. The self-assembly results in the formation of a well-ordered threedimensional body-centered tetragonal quantum dot lattice within the whole deposited volume. The quantum dots formed are very small in size less than 4.0 nm, have a narrow size distribution and a large packing density. The parameters of the quantum dot lattice can be tuned by changing the deposition parameters. The self-ordering of the quantum dots is explained by diffusionmediated nucleation and surface-morphology effects and simulated by a kinetic Monte Carlo model.

Published
2025
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3. Effect of Pt bottom electrode texture selection on the tetragonality and physical properties of Ba0.8Sr0.2TiO3 thin films produced by pulsed laser deposition

Author

Silva, J. P. B., Sekhar, K. C., Almeida, A., Moreira, J. Agostinho, Martín-Sánchez, J., Pereira, M., Khodorov, A., and Gomes, M. J. M.

Subjects
Condensed Matter - Materials Science
Abstract

The effect of platinum (Pt) bottom electrode texture on the tetragonality, dielectric, ferroelectric, and polarization switching response of pulsed laser deposited Ba0.8Sr0.2TiO3 (BST) thin films has been studied. The x-ray diffraction and Raman analysis revealed the higher tetragonality of BST films when they were grown on higher (111) textured Pt layer. The properties like dielectric permittivity, polarization, switching time, and leakage currents were found to be correlated to tetragonality and orientation of the BST films. The polarization current was observed to be higher in BST films on Pt epitaxial layer and it exhibits exponential dependence on the electric field. The voltage-current measurements displayed Ohmic behavior of leakage current irrespective of Pt texture for low voltages (up to 1 V), whereas at higher voltages the conduction mechanism was found to be dependent on texture selection of bottom Pt electrode., Comment: 23 pages, 14 figures

Published
2025
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4. Complexity of Deciding the Equality of Matching Numbers

Author

Gomes, Guilherme C. M., Masquio, Bruno P., Pinto, Paulo E. D., Rautenbach, Dieter, Santos, Vinicius F. dos, Szwarcfiter, Jayme L., and Werner, Florian

Subjects
Computer Science - Discrete Mathematics
Abstract

A matching is said to be disconnected if the saturated vertices induce a disconnected subgraph and induced if the saturated vertices induce a 1-regular graph. The disconnected and induced matching numbers are defined as the maximum cardinality of such matchings, respectively, and are known to be NP-hard to compute. In this paper, we study the relationship between these two parameters and the matching number. In particular, we discuss the complexity of two decision problems; first: deciding if the matching number and disconnected matching number are equal; second: deciding if the disconnected matching number and induced matching number are equal. We show that given a bipartite graph with diameter four, deciding if the matching number and disconnected matching number are equal is NP-complete; the same holds for bipartite graphs with maximum degree three. We characterize diameter three graphs with equal matching number and disconnected matching number, which yields a polynomial time recognition algorithm. Afterwards, we show that deciding if the induced and disconnected matching numbers are equal is co-NP-complete for bipartite graphs of diameter 3. When the induced matching number is large enough compared to the maximum degree, we characterize graphs where these parameters are equal, which results in a polynomial time algorithm for bounded degree graphs.

Published
2024

5. Matching (Multi)Cut: Algorithms, Complexity, and Enumeration

Author

Gomes, Guilherme C. M., Juliano, Emanuel, Martins, Gabriel, and Santos, Vinicius F. dos

Subjects
Computer Science - Data Structures and Algorithms
Abstract

A matching cut of a graph is a partition of its vertex set in two such that no vertex has more than one neighbor across the cut. The Matching Cut problem asks if a graph has a matching cut. This problem, and its generalization d-cut, has drawn considerable attention of the algorithms and complexity community in the last decade, becoming a canonical example for parameterized enumeration algorithms and kernelization. In this paper, we introduce and study a generalization of Matching Cut, which we have named Matching Multicut: can we partition the vertex set of a graph in at least $\ell$ parts such that no vertex has more than one neighbor outside its part? We investigate this question in several settings. We start by showing that, contrary to Matching Cut, it is NP-hard on cubic graphs but that, when $\ell$ is a parameter, it admits a quasi-linear kernel. We also show an $O(\ell^{\frac{n}{2}})$ time exact exponential algorithm for general graphs and a $2^{O(t \log t)}n^{O(1)}$ time algorithm for graphs of treewidth at most $t$. We then study parameterized enumeration aspects of matching multicuts. First, we generalize the quadratic kernel of Golovach et. al for Enum Matching Cut parameterized by vertex cover, then use it to design a quadratic kernel for Enum Matching (Multi)cut parameterized by vertex-deletion distance to co-cluster. Our final contributions are on the vertex-deletion distance to cluster parameterization, where we show an FPT-delay algorithm for Enum Matching Multicut but that no polynomial kernel exists unless NP $\subseteq$ coNP/poly; we highlight that we have no such lower bound for Enum Matching Cut and consider it our main open question.

Published
2024

8. Visual Search in People with Macular Degeneration: A Virtual Reality Eye-Tracking Study

Author

Kempapidis, Theofilos, Mavridou, Ifigeneia, Seiss, Ellen, Castle, Claire L., Bradwell, Daisy, Panchevski, Filip, Cox, Sophia, Gomes, Renata S. M., Goos, Gerhard, Series Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Reyes-Lecuona, Arcadio, editor, Zachmann, Gabriel, editor, Bordegoni, Monica, editor, Chen, Jian, editor, Karaseitanidis, Giannis, editor, Pagani, Alain, editor, and Bourdot, Patrick, editor

Published
2025
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11. Latitudinal gradients in seed predation persist in urbanized environments

Author

Hargreaves, Anna L., Ensing, John, Rahn, Olivia, Oliveira, Fernanda M. P., Burkiewicz, Jérôme, Lafond, Joëlle, Haeussler, Sybille, Byerley-Best, M. Brooke, Lazda, Kira, Slinn, Heather L., Martin, Ella, Carlson, Matthew L., Sformo, Todd L., Dawson-Glass, Emma, Chiuffo, Mariana C., Vargas-Rodriguez, Yalma L., García-Jiménez, Carlos I., Gomes, Inácio J. M. T., Klemet-N’Guessan, Sandra, Paolucci, Lucas, Joly, Simon, Mehltreter, Klaus, Muñoz, Jenny, Buono, Carmela, Brodie, Jedediah F., Rodriguez-Campbell, Antonio, Veen, Thor, Freeman, Benjamin G., Lee-Yaw, Julie A., Muñoz, Juan Camilo, Paquette, Alexandra, Butler, Jennifer, and Suaréz, Esteban

Published
2024
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12. Solving the Discretised Multiphase Flow Equations with Interface Capturing on Structured Grids Using Machine Learning Libraries

Author

Chen, Boyang, Heaney, Claire E., Gomes, Jefferson L. M. A., Matar, Omar K., and Pain, Christopher C.

Subjects
Physics - Fluid Dynamics, Computer Science - Machine Learning
Abstract

This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network whose weights are determined by the numerical method, rather than by training, and hence, we refer to this approach as Neural Networks for PDEs (NN4PDEs). To solve the discretised multiphase flow equations, a multigrid solver is implemented through a convolutional neural network with a U-Net architecture. Immiscible two-phase flow is modelled by the 3D incompressible Navier-Stokes equations with surface tension and advection of a volume fraction field, which describes the interface between the fluids. A new compressive algebraic volume-of-fluids method is introduced, based on a residual formulation using Petrov-Galerkin for accuracy and designed with NN4PDEs in mind. High-order finite-element based schemes are chosen to model a collapsing water column and a rising bubble. Results compare well with experimental data and other numerical results from the literature, demonstrating that, for the first time, finite element discretisations of multiphase flows can be solved using an approach based on (untrained) convolutional neural networks. A benefit of expressing numerical discretisations as neural networks is that the code can run, without modification, on CPUs, GPUs or the latest accelerators designed especially to run AI codes., Comment: 34 pages, 18 figures, 4 tables

Published
2024
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13. An efficient topology optimization algorithm for large-scale three-dimensional structures

Author

Vitorino, Alfredo and Gomes, Francisco A. M.

Subjects
Mathematics - Optimization and Control, 74B05, 90C30, 65K05, 65F10
Abstract

Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems. The robustness of the algorithm is ensured by adopting a globally convergent sequential linear programming method with a stopping criterion based on the first-order optimality conditions of the nonlinear problem. To increase the algorithm's efficiency, it is combined with a multiresolution scheme that employs different discretizations to deal with displacement, design, and density variables. In addition, the time spent solving the linear equilibrium systems is substantially reduced using multigrid as a preconditioner for the conjugate gradient method. Since multiresolution can lead to the appearance of unwanted artefacts in the structure, we propose an adaptive strategy for increasing the degree of the displacement elements, with a technique for suppressing unnecessary variables that provides accurate solutions with a moderate impact on the algorithm's performance. We also propose a new thresholding strategy, based on gradient information, to obtain structures composed only by solid or void regions. Computational experiments carried out in Matlab prove that the new algorithm effectively generates high-resolution structures at a low computational cost.

Published
2023

14. Minimum Separator Reconfiguration

Author

Gomes, Guilherme C. M., Legrand-Duchesne, Clément, Mahmoud, Reem, Mouawad, Amer E., Okamoto, Yoshio, Santos, Vinicius F. dos, and van der Zanden, Tom C.

Subjects
Computer Science - Computational Complexity, Computer Science - Discrete Mathematics, Mathematics - Combinatorics
Abstract

We study the problem of reconfiguring one minimum $s$-$t$-separator $A$ into another minimum $s$-$t$-separator $B$ in some $n$-vertex graph $G$ containing two non-adjacent vertices $s$ and $t$. We consider several variants of the problem as we focus on both the token sliding and token jumping models. Our first contribution is a polynomial-time algorithm that computes (if one exists) a minimum-length sequence of slides transforming $A$ into $B$. We additionally establish that the existence of a sequence of jumps (which need not be of minimum length) can be decided in polynomial time (by an algorithm that also outputs a witnessing sequence when one exists). In contrast, and somewhat surprisingly, we show that deciding if a sequence of at most $\ell$ jumps can transform $A$ into $B$ is an $\textsf{NP}$-complete problem. To complement this negative result, we investigate the parameterized complexity of what we believe to be the two most natural parameterized counterparts of the latter problem; in particular, we study the problem of computing a minimum-length sequence of jumps when parameterized by the size $k$ of the minimum \stseps and when parameterized by the number of jumps $\ell$. For the first parameterization, we show that the problem is fixed-parameter tractable, but does not admit a polynomial kernel unless $\textsf{NP} \subseteq \textsf{coNP/poly}$. We complete the picture by designing a kernel with $\mathcal{O}(\ell^2)$ vertices and edges for the length $\ell$ of the sequence as a parameter., Comment: 37 pages, 9 figures

Published
2023

19. Power System Plant and Network Dynamic Model Validation

Author

Modi, Nilesh, Grogan, Sorrell, Bélanger, Jean, Badrzadeh, Babak, Lietz, Genevieve, Halley, Andrew, Dennetière, Sébastien, Zhang, Qiang “Frankie”, Jacobson, David, Heydari, Rasool, Gomes Guerreiro, Gabriel M., CIGRE, Series Editor, Badrzadeh, Babak, editor, and Emin, Zia, editor

Published
2024
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22. Weighted Connected Matchings

Author

Gomes, Guilherme C. M., Masquio, Bruno P., Pinto, Paulo E. D., Santos, Vinicius F. dos, and Szwarcfiter, Jayme L.

Subjects
Computer Science - Discrete Mathematics
Abstract

A matching $M$ is a $\mathscr{P}$-matching if the subgraph induced by the endpoints of the edges of $M$ satisfies property $\mathscr{P}$. As examples, for appropriate choices of $\mathscr{P}$, the problems Induced Matching, Uniquely Restricted Matching, Connected Matching and Disconnected Matching arise. For many of these problems, finding a maximum $\mathscr{P}$-matching is a knowingly NP-Hard problem, with few exceptions, such as connected matchings, which has the same time complexity as usual Maximum Matching problem. The weighted variant of Maximum Matching has been studied for decades, with many applications, including the well-known Assignment problem. Motivated by this fact, in addition to some recent researches in weighted versions of acyclic and induced matchings, we study the Maximum Weight Connected Matching. In this problem, we want to find a matching $M$ such that the endpoint vertices of its edges induce a connected subgraph and the sum of the edge weights of $M$ is maximum. Unlike the unweighted Connected Matching problem, which is in P for general graphs, we show that Maximum Weight Connected Matching is NP-Hard even for bounded diameter bipartite graphs, starlike graphs, planar bipartite, and bounded degree planar graphs, while solvable in linear time for trees and subcubic graphs. When we restrict edge weights to be non negative only, we show that the problem turns to be polynomially solvable for chordal graphs, while it remains NP-Hard for most of the cases when weights can be negative. Our final contributions are on parameterized complexity. On the positive side, we present a single exponential time algorithm when parameterized by treewidth. In terms of kernelization, we show that, even when restricted to binary weights, Weighted Connected Matching does not admit a polynomial kernel when parameterized by vertex cover under standard complexity-theoretical hypotheses.

Published
2022

26. Disconnected Matchings

Author

Gomes, Guilherme C. M., Masquio, Bruno P., Pinto, Paulo E. D., Santos, Vinicius F. dos, and Szwarcfiter, Jayme L.

Subjects
Computer Science - Discrete Mathematics, Computer Science - Data Structures and Algorithms
Abstract

In 2005, Goddard, Hedetniemi, Hedetniemi and Laskar [Generalized subgraph-restricted matchings in graphs, Discrete Mathematics, 293 (2005) 129 - 138] asked the computational complexity of determining the maximum cardinality of a matching whose vertex set induces a disconnected graph. In this paper we answer this question. In fact, we consider the generalized problem of finding $c$-disconnected matchings; such matchings are ones whose vertex sets induce subgraphs with at least $c$ connected components. We show that, for every fixed $c \geq 2$, this problem is NP-complete even if we restrict the input to bounded diameter bipartite graphs, while can be solved in polynomial time if $c = 1$. For the case when $c$ is part of the input, we show that the problem is NP-complete for chordal graphs, while being solvable in polynomial time for interval graphs. Finally, we explore the parameterized complexity of the problem. We present an FPT algorithm under the treewidth parameterization, and an XP algorithm for graphs with a polynomial number of minimal separators when parameterized by $c$. We complement these results by showing that, unless NP $\subseteq$ coNP/poly, the related Induced Matching problem does not admit a polynomial kernel when parameterized by vertex cover and size of the matching nor when parameterized by vertex deletion distance to clique and size of the matching. As for Connected Matching, we show how to obtain a maximum connected matching in linear time given an arbitrary maximum matching in the input.

Published
2021

27. Inexact Newton combined approximations in the topology optimization of geometrically nonlinear elastic structures and compliant mechanisms

Author

Senne, Thadeu A., Gomes, Francisco A. M., and Santos, Sandra A.

Subjects
Mathematics - Numerical Analysis, Mathematics - Optimization and Control, 90C30, 65K05, 47J25, 65J15, 74B20
Abstract

This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a sequential piecewise linear programming (SPLP) algorithm. Five distinct strategies have been proposed to control the frequency of the factorizations of the Jacobian matrices of the nonlinear equilibrium equations. Aiming at speeding up the overall iterative scheme while keeping the accuracy of the approximate solutions, three of the strategies also use an ICA scheme for the adjoint linear system associated with the sensitivity analysis. The robustness of the proposed reanalysis strategies is corroborated by means of numerical experiments with four benchmark problems -- two structures and two compliant mechanisms. Besides assessing the performance of the strategies considering a fixed budget of iterations, the impact of a theoretically supported stopping criterion for the SPLP algorithm was analyzed as well.

Published
2021

29. Global burden and strength of evidence for 88 risk factors in 204 countries and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

Author

Brauer, Michael, Roth, Gregory A, Aravkin, Aleksandr Y, Zheng, Peng, Abate, Kalkidan Hassen, Abate, Yohannes Habtegiorgis, Abbafati, Cristiana, Abbasgholizadeh, Rouzbeh, Abbasi, Madineh Akram, Abbasian, Mohammadreza, Abbasifard, Mitra, Abbasi-Kangevari, Mohsen, Abd ElHafeez, Samar, Abd-Elsalam, Sherief, Abdi, Parsa, Abdollahi, Mohammad, Abdoun, Meriem, Abdulah, Deldar Morad, Abdullahi, Auwal, Abebe, Mesfin, Abedi, Aidin, Abedi, Armita, Abegaz, Tadesse M, Abeldaño Zuñiga, Roberto Ariel, Abiodun, Olumide, Abiso, Temesgen Lera, Aboagye, Richard Gyan, Abolhassani, Hassan, Abouzid, Mohamed, Aboye, Girma Beressa, Abreu, Lucas Guimarães, Abualruz, Hasan, Abubakar, Bilyaminu, Abu-Gharbieh, Eman, Abukhadijah, Hana Jihad Jihad, Aburuz, Salahdein, Abu-Zaid, Ahmed, Adane, Mesafint Molla, Addo, Isaac Yeboah, Addolorato, Giovanni, Adedoyin, Rufus Adesoji, Adekanmbi, Victor, Aden, Bashir, Adetunji, Juliana Bunmi, Adeyeoluwa, Temitayo Esther, Adha, Rishan, Adibi, Amin, Adnani, Qorinah Estiningtyas Sakilah, Adzigbli, Leticia Akua, Afolabi, Aanuoluwapo Adeyimika, Afolabi, Rotimi Felix, Afshin, Ashkan, Afyouni, Shadi, Afzal, Muhammad Sohail, Afzal, Saira, Agampodi, Suneth Buddhika, Agbozo, Faith, Aghamiri, Shahin, Agodi, Antonella, Agrawal, Anurag, Agyemang-Duah, Williams, Ahinkorah, Bright Opoku, Ahmad, Aqeel, Ahmad, Danish, Ahmad, Firdos, Ahmad, Noah, Ahmad, Shahzaib, Ahmad, Tauseef, Ahmed, Ali, Ahmed, Anisuddin, Ahmed, Ayman, Ahmed, Luai A, Ahmed, Muktar Beshir, Ahmed, Safoora, Ahmed, Syed Anees, Ajami, Marjan, Akalu, Gizachew Taddesse, Akara, Essona Matatom, Akbarialiabad, Hossein, Akhlaghi, Shiva, Akinosoglou, Karolina, Akinyemiju, Tomi, Akkaif, Mohammed Ahmed, Akkala, Sreelatha, Akombi-Inyang, Blessing, Al Awaidy, Salah, Al Hasan, Syed Mahfuz, Alahdab, Fares, AL-Ahdal, Tareq Mohammed Ali, Alalalmeh, Samer O, Alalwan, Tariq A, Al-Aly, Ziyad, Alam, Khurshid, Alam, Nazmul, Alanezi, Fahad Mashhour, Alanzi, Turki M, Albakri, Almaza, AlBataineh, Mohammad T, Aldhaleei, Wafa A, Aldridge, Robert W, Alemayohu, Mulubirhan Assefa, Alemu, Yihun Mulugeta, Al-Fatly, Bassam, Al-Gheethi, Adel Ali Saeed, Al-Habbal, Khairat, Alhabib, Khalid F, Alhassan, Robert Kaba, Ali, Abid, Ali, Amjad, Ali, Beriwan Abdulqadir, Ali, Iman, Ali, Liaqat, Ali, Mohammed Usman, Ali, Rafat, Ali, Syed Shujait Shujait, Ali, Waad, Alicandro, Gianfranco, Alif, Sheikh Mohammad, Aljunid, Syed Mohamed, Alla, François, Al-Marwani, Sabah, Al-Mekhlafi, Hesham M, Almustanyir, Sami, Alomari, Mahmoud A, Alonso, Jordi, Alqahtani, Jaber S, Alqutaibi, Ahmed Yaseen, Al-Raddadi, Rajaa M, Alrawashdeh, Ahmad, Al-Rifai, Rami Hani, Alrousan, Sahel Majed, Al-Sabah, Salman Khalifah, Alshahrani, Najim Z, Altaany, Zaid, Altaf, Awais, Al-Tawfiq, Jaffar A, Altirkawi, Khalid A, Aluh, Deborah Oyine, Alvis-Guzman, Nelson, Alvis-Zakzuk, Nelson J, Alwafi, Hassan, Al-Wardat, Mohammad Sami, Al-Worafi, Yaser Mohammed, Aly, Hany, Aly, Safwat, Alzoubi, Karem H, Al-Zyoud, Walid, Amaechi, Uchenna Anderson, Aman Mohammadi, Masous, Amani, Reza, Amiri, Sohrab, Amirzade-Iranaq, Mohammad Hosein, Ammirati, Enrico, Amu, Hubert, Amugsi, Dickson A, Amusa, Ganiyu Adeniyi, Ancuceanu, Robert, Anderlini, Deanna, Anderson, Jason A, Andrade, Pedro Prata, Andrei, Catalina Liliana, Andrei, Tudorel, Anenberg, Susan C, Angappan, Dhanalakshmi, Angus, Colin, Anil, Abhishek, Anil, Sneha, Anjum, Afifa, Anoushiravani, Amir, Antonazzo, Ippazio Cosimo, Antony, Catherine M, Antriyandarti, Ernoiz, Anuoluwa, Boluwatife Stephen, Anvari, Davood, Anvari, Saeid, Anwar, Saleha, Anwar, Sumadi Lukman, Anwer, Razique, Anyabolo, Ekenedilichukwu Emmanuel, Anyasodor, Anayochukwu Edward, Apostol, Geminn Louis Carace, Arabloo, Jalal, Arabzadeh Bahri, Razman, Arafat, Mosab, Areda, Demelash, Aregawi, Brhane Berhe, Aremu, Abdulfatai, Armocida, Benedetta, Arndt, Michael Benjamin, Ärnlöv, Johan, Arooj, Mahwish, Artamonov, Anton A, Artanti, Kurnia Dwi, Aruleba, Idowu Thomas, Arumugam, Ashokan, Asbeutah, Akram M, Asgary, Saeed, Asgedom, Akeza Awealom, Ashbaugh, Charlie, Ashemo, Mubarek Yesse, Ashraf, Tahira, Askarinejad, Amir, Assmus, Michael, Astell-Burt, Thomas, Athar, Mohammad, Athari, Seyyed Shamsadin, Atorkey, Prince, Atreya, Alok, Aujayeb, Avinash, Ausloos, Marcel, Avila-Burgos, Leticia, Awoke, Andargie Abate, Ayala Quintanilla, Beatriz Paulina, Ayatollahi, Haleh, Ayestas Portugal, Carlos, Ayuso-Mateos, Jose L, Azadnajafabad, Sina, Azevedo, Rui M S, Azhar, Gulrez Shah, Azizi, Hosein, Azzam, Ahmed Y, Backhaus, Insa Linnea, Badar, Muhammad, Badiye, Ashish D, Bagga, Arvind, Baghdadi, Soroush, Bagheri, Nasser, Bagherieh, Sara, Bahrami Taghanaki, Pegah, Bai, Ruhai, Baig, Atif Amin, Baker, Jennifer L, Bakkannavar, Shankar M, Balasubramanian, Madhan, Baltatu, Ovidiu Constantin, Bam, Kiran, Bandyopadhyay, Soham, Banik, Biswajit, Banik, Palash Chandra, Banke-Thomas, Aduragbemi, Bansal, Hansi, Barchitta, Martina, Bardhan, Mainak, Bardideh, Erfan, Barker-Collo, Suzanne Lyn, Bärnighausen, Till Winfried, Barone-Adesi, Francesco, Barqawi, Hiba Jawdat, Barrero, Lope H, Barrow, Amadou, Barteit, Sandra, Basharat, Zarrin, Basiru, Afisu, Basso, João Diogo, Bastan, Mohammad-Mahdi, Basu, Sanjay, Batchu, Sai, Batra, Kavita, Batra, Ravi, Baune, Bernhard T, Bayati, Mohsen, Bayileyegn, Nebiyou Simegnew, Beaney, Thomas, Behnoush, Amir Hossein, Beiranvand, Maryam, Béjot, Yannick, Bekele, Alehegn, Belgaumi, Uzma Iqbal, Bell, Arielle Wilder, Bell, Michelle L, Bello, Muhammad Bashir, Bello, Olorunjuwon Omolaja, Belo, Luis, Beloukas, Apostolos, Bendak, Salaheddine, Bennett, Derrick A, Bennitt, Fiona B, Bensenor, Isabela M, Benzian, Habib, Beran, Azizullah, Berezvai, Zombor, Bernabe, Eduardo, Bernstein, Robert S, Bettencourt, Paulo J G, Bhagavathula, Akshaya Srikanth, Bhala, Neeraj, Bhandari, Dinesh, Bhardwaj, Nikha, Bhardwaj, Pankaj, Bhaskar, Sonu, Bhat, Ajay Nagesh, Bhat, Vivek, Bhatti, Gurjit Kaur, Bhatti, Jasvinder Singh, Bhatti, Manpreet S, Bhatti, Rajbir, Bhuiyan, Mohiuddin Ahmed, Bhutta, Zulfiqar A, Bikbov, Boris, Bishai, Jessica Devin, Bisignano, Catherine, Biswas, Atanu, Biswas, Bijit, Biswas, Raaj Kishore, Bjørge, Tone, Boachie, Micheal Kofi, Boakye, Hosea, Bockarie, Moses John, Bodolica, Virginia, Bodunrin, Aadam Olalekan, Bogale, Eyob Ketema, Bolla, Srinivasa Rao, Boloor, Archith, Bonakdar Hashemi, Milad, Boppana, Sri Harsha, Bora Basara, Berrak, Borhany, Hamed, Botero Carvajal, Alejandro, Bouaoud, Souad, Boufous, Soufiane, Bourne, Rupert, Boxe, Christopher, Braithwaite, Dejana, Brant, Luisa C, Brar, Amanpreet, Breitborde, Nicholas J K, Breitner, Susanne, Brenner, Hermann, Briko, Andrey Nikolaevich, Britton, Gabrielle, Brown, Colin Stewart, Browne, Annie J, Brunoni, Andre R, Bryazka, Dana, Bulamu, Norma B, Bulto, Lemma N, Buonsenso, Danilo, Burkart, Katrin, Burns, Richard A, Busse, Reinhard, Bustanji, Yasser, Butt, Nadeem Shafique, Butt, Zahid A, Caetano dos Santos, Florentino Luciano, Cagney, Jack, Cahuana-Hurtado, Lucero, Calina, Daniela, Cámera, Luis Alberto, Campos, Luciana Aparecida, Campos-Nonato, Ismael R, Cao, Chao, Cao, Fan, Cao, Yubin, Capodici, Angelo, Cárdenas, Rosario, Carr, Sinclair, Carreras, Giulia, Carrero, Juan J, Carugno, Andrea, Carvalho, Felix, Carvalho, Márcia, Castaldelli-Maia, Joao Mauricio, Castañeda-Orjuela, Carlos A, Castelpietra, Giulio, Catalá-López, Ferrán, Catapano, Alberico L, Cattaruzza, Maria Sofia, Caye, Arthur, Cederroth, Christopher R, Cegolon, Luca, Cenderadewi, Muthia, Cercy, Kelly M, Cerin, Ester, Chadwick, Joshua, Chakraborty, Chiranjib, Chakraborty, Promit Ananyo, Chakraborty, Sandip, Chan, Jeffrey Shi Kai, Chan, Raymond N C, Chandan, Joht Singh, Chandika, Rama Mohan, Chaturvedi, Pankaj, Chen, An-Tian, Chen, Catherine S, Chen, Haowei, Chen, Meng Xuan, Chen, Mingling, Chen, Simiao, Cheng, Ching-Yu, Cheng, Esther T W, Cherbuin, Nicolas, Chi, Gerald, Chichagi, Fatemeh, Chimed-Ochir, Odgerel, Chimoriya, Ritesh, Ching, Patrick R, Chirinos-Caceres, Jesus Lorenzo, Chitheer, Abdulaal, Cho, William C S, Chong, Bryan, Chopra, Hitesh, Chowdhury, Rajiv, 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Samer H, Murray, Christopher J L, and Gakidou, Emmanuela

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2024
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30. Global burden of 288 causes of death and life expectancy decomposition in 204 countries and territories and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

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Naghavi, Mohsen, Ong, Kanyin Liane, Aali, Amirali, Ababneh, Hazim S, Abate, Yohannes Habtegiorgis, Abbafati, Cristiana, Abbasgholizadeh, Rouzbeh, Abbasian, Mohammadreza, Abbasi-Kangevari, Mohsen, Abbastabar, Hedayat, Abd ElHafeez, Samar, Abdelmasseh, Michael, Abd-Elsalam, Sherief, Abdelwahab, Ahmed, Abdollahi, Mohammad, Abdollahifar, Mohammad-Amin, Abdoun, Meriem, Abdulah, Deldar Morad, Abdullahi, Auwal, Abebe, Mesfin, Abebe, Samrawit Shawel, Abedi, Aidin, Abegaz, Kedir Hussein, Abhilash, E S, Abidi, Hassan, Abiodun, Olumide, Aboagye, Richard Gyan, Abolhassani, Hassan, Abolmaali, Meysam, Abouzid, Mohamed, Aboye, Girma Beressa, Abreu, Lucas Guimarães, Abrha, Woldu Aberhe, Abtahi, Dariush, Abu Rumeileh, Samir, Abualruz, Hasan, Abubakar, Bilyaminu, Abu-Gharbieh, Eman, Abu-Rmeileh, Niveen ME, Aburuz, Salahdein, Abu-Zaid, Ahmed, Accrombessi, Manfred Mario Kokou, Adal, Tadele Girum, Adamu, Abdu A, Addo, Isaac Yeboah, Addolorato, Giovanni, Adebiyi, Akindele Olupelumi, Adekanmbi, Victor, Adepoju, Abiola Victor, Adetunji, Charles Oluwaseun, Adetunji, Juliana Bunmi, Adeyeoluwa, Temitayo Esther, Adeyinka, Daniel Adedayo, Adeyomoye, Olorunsola Israel, Admass, Biruk Adie Adie, Adnani, Qorinah Estiningtyas Sakilah, Adra, Saryia, Afolabi, Aanuoluwapo Adeyimika, Afzal, Muhammad Sohail, Afzal, Saira, Agampodi, Suneth Buddhika, Agasthi, Pradyumna, Aggarwal, Manik, Aghamiri, Shahin, Agide, Feleke Doyore, Agodi, Antonella, Agrawal, Anurag, Agyemang-Duah, Williams, Ahinkorah, Bright Opoku, Ahmad, Aqeel, Ahmad, Danish, Ahmad, Firdos, Ahmad, Muayyad M, Ahmad, Sajjad, Ahmad, Shahzaib, Ahmad, Tauseef, Ahmadi, Keivan, Ahmadzade, Amir Mahmoud, Ahmed, Ali, Ahmed, Ayman, Ahmed, Haroon, Ahmed, Luai A, Ahmed, Mehrunnisha Sharif, Ahmed, Meqdad Saleh, Ahmed, Muktar Beshir, Ahmed, Syed Anees, Ajami, Marjan, Aji, Budi, Akara, Essona Matatom, Akbarialiabad, Hossein, Akinosoglou, Karolina, Akinyemiju, Tomi, Akkaif, Mohammed Ahmed, Akyirem, Samuel, Al Hamad, Hanadi, Al Hasan, Syed Mahfuz, Alahdab, Fares, Alalalmeh, Samer O, Alalwan, Tariq A, Al-Aly, Ziyad, Alam, Khurshid, Alam, Manjurul, Alam, Noore, Al-amer, Rasmieh Mustafa, Alanezi, Fahad Mashhour, Alanzi, Turki M, Al-Azzam, Sayer, Albakri, Almaza, Albashtawy, Mohammed, AlBataineh, Mohammad T, Alcalde-Rabanal, Jacqueline Elizabeth, Aldawsari, Khalifah A, Aldhaleei, Wafa A, Aldridge, Robert W, Alema, Haileselasie Berhane, Alemayohu, Mulubirhan Assefa, Alemi, Sharifullah, Alemu, Yihun Mulugeta, Al-Gheethi, Adel Ali Saeed, Alhabib, Khalid F, Alhalaiqa, Fadwa Alhalaiqa Naji, Al-Hanawi, Mohammed Khaled, Ali, Abid, Ali, Amjad, Ali, Liaqat, Ali, Mohammed Usman, Ali, Rafat, Ali, Shahid, Ali, Syed Shujait Shujait, Alicandro, Gianfranco, Alif, Sheikh Mohammad, Alikhani, Reyhaneh, Alimohamadi, Yousef, Aliyi, Ahmednur Adem, Aljasir, Mohammad A M, Aljunid, Syed Mohamed, Alla, François, Allebeck, Peter, Al-Marwani, Sabah, Al-Maweri, Sadeq Ali Ali, Almazan, Joseph Uy, Al-Mekhlafi, Hesham M, Almidani, Louay, Almidani, Omar, Alomari, Mahmoud A, Al-Omari, Basem, Alonso, Jordi, Alqahtani, Jaber S, Alqalyoobi, Shehabaldin, Alqutaibi, Ahmed Yaseen, Al-Sabah, Salman Khalifah, Altaany, Zaid, Altaf, Awais, Al-Tawfiq, Jaffar A, Altirkawi, Khalid A, Aluh, Deborah Oyine, Alvis-Guzman, Nelson, Alwafi, Hassan, Al-Worafi, Yaser Mohammed, Aly, Hany, Aly, Safwat, Alzoubi, Karem H, Amani, Reza, Amare, Azmeraw T, Amegbor, Prince M, Ameyaw, Edward Kwabena, Amin, Tarek Tawfik, Amindarolzarbi, Alireza, Amiri, Sohrab, Amirzade-Iranaq, Mohammad Hosein, Amu, Hubert, Amugsi, Dickson A, Amusa, Ganiyu Adeniyi, Ancuceanu, Robert, Anderlini, Deanna, Anderson, David B, Andrade, Pedro Prata, Andrei, Catalina Liliana, Andrei, Tudorel, Angus, Colin, Anil, Abhishek, Anil, Sneha, Anoushiravani, Amir, Ansari, Hossein, Ansariadi, Ansariadi, Ansari-Moghaddam, Alireza, Antony, Catherine M, Antriyandarti, Ernoiz, Anvari, Davood, Anvari, Saeid, Anwar, Saleha, Anwar, Sumadi Lukman, Anwer, Razique, Anyasodor, Anayochukwu Edward, Aqeel, Muhammad, Arab, Juan Pablo, Arabloo, Jalal, Arafat, Mosab, Aravkin, Aleksandr Y, Areda, Demelash, Aremu, Abdulfatai, Aremu, Olatunde, Ariffin, Hany, Arkew, Mesay, Armocida, Benedetta, Arndt, Michael Benjamin, Ärnlöv, Johan, Arooj, Mahwish, Artamonov, Anton A, Arulappan, Judie, Aruleba, Raphael Taiwo, Arumugam, Ashokan, Asaad, Malke, Asadi-Lari, Mohsen, Asgedom, Akeza Awealom, Asghariahmadabad, Mona, Asghari-Jafarabadi, Mohammad, Ashraf, Muhammad, Aslani, Armin, Astell-Burt, Thomas, Athar, Mohammad, Athari, Seyyed Shamsadin, Atinafu, Bantalem Tilaye Tilaye, Atlaw, Habtamu Wondmagegn, Atorkey, Prince, Atout, Maha Moh'd Wahbi, Atreya, Alok, Aujayeb, Avinash, Ausloos, Marcel, Avan, Abolfazl, Awedew, Atalel Fentahun, Aweke, Amlaku Mulat, Ayala Quintanilla, Beatriz Paulina, Ayatollahi, Haleh, Ayuso-Mateos, Jose L, Ayyoubzadeh, Seyed Mohammad, Azadnajafabad, Sina, Azevedo, Rui M S, Azzam, Ahmed Y, B, Darshan B, Babu, Abraham Samuel, Badar, Muhammad, Badiye, Ashish D, Baghdadi, Soroush, Bagheri, Nasser, Bagherieh, Sara, Bah, Sulaiman, Bahadorikhalili, Saeed, Bahmanziari, Najmeh, Bai, Ruhai, Baig, Atif Amin, Baker, Jennifer L, Bako, Abdulaziz T, Bakshi, Ravleen Kaur, Balakrishnan, Senthilkumar, Balasubramanian, Madhan, Baltatu, Ovidiu Constantin, Bam, Kiran, Banach, Maciej, Bandyopadhyay, Soham, Banik, Palash Chandra, Bansal, Hansi, Bansal, Kannu, Barbic, Franca, Barchitta, Martina, Bardhan, Mainak, Bardideh, Erfan, Barker-Collo, Suzanne Lyn, Bärnighausen, Till Winfried, Barone-Adesi, Francesco, Barqawi, Hiba Jawdat, Barrero, Lope H, Barrow, Amadou, Barteit, Sandra, Barua, Lingkan, Basharat, Zarrin, Bashiri, Azadeh, Basiru, Afisu, Baskaran, Pritish, Basnyat, Buddha, Bassat, Quique, Basso, João Diogo, Basting, Ann V L, Basu, Sanjay, Batra, Kavita, Baune, Bernhard T, Bayati, Mohsen, Bayileyegn, Nebiyou Simegnew, Beaney, Thomas, Bedi, Neeraj, Beghi, Massimiliano, Behboudi, Emad, Behera, Priyamadhaba, Behnoush, Amir Hossein, Behzadifar, Masoud, Beiranvand, Maryam, Bejarano Ramirez, Diana Fernanda, Béjot, 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Maureene Auma, Ong, Sokking, Onwujekwe, Obinna E, Onyedibe, Kenneth Ikenna, Ordak, Michal, Orisakwe, Orish Ebere, Orish, Verner N, Ortega-Altamirano, Doris V, Ortiz, Alberto, Osman, Wael M S, Ostroff, Samuel M, Osuagwu, Uchechukwu Levi, Otoiu, Adrian, Otstavnov, Nikita, Otstavnov, Stanislav S, Ouyahia, Amel, Ouyang, Guoqing, Owolabi, Mayowa O, Ozten, Yaz, P A, Mahesh Padukudru, Padron-Monedero, Alicia, Padubidri, Jagadish Rao, Pal, Pramod Kumar, Palicz, Tamás, Palladino, Claudia, Palladino, Raffaele, Palma-Alvarez, Raul Felipe, Pan, Feng, Pan, Hai-Feng, Pana, Adrian, Panda, Paramjot, Panda-Jonas, Songhomitra, Pandi-Perumal, Seithikurippu R, Pangaribuan, Helena Ullyartha, Panos, Georgios D, Panos, Leonidas D, Pantazopoulos, Ioannis, Pantea Stoian, Anca Mihaela, Papadopoulou, Paraskevi, Parikh, Romil R, Park, Seoyeon, Parthasarathi, Ashwaghosha, Pashaei, Ava, Pasovic, Maja, Passera, Roberto, Pasupula, Deepak Kumar, Patel, Hemal M, Patel, Jay, Patel, Sangram Kishor, Patil, Shankargouda, Patoulias, Dimitrios, Patthipati, Venkata Suresh, Paudel, Uttam, Pazoki Toroudi, Hamidreza, Pease, Spencer A, Peden, Amy E, Pedersini, Paolo, Pensato, Umberto, Pepito, Veincent Christian Filipino, Peprah, Emmanuel K, Peprah, Prince, Perdigão, João, Pereira, Marcos, Peres, Mario F P, Perianayagam, Arokiasamy, Perico, Norberto, Pestell, Richard G, Pesudovs, Konrad, Petermann-Rocha, Fanny Emily, Petri, William A, Pham, Hoang Tran, Philip, Anil K, Phillips, Michael R, Pierannunzio, Daniela, Pigeolet, Manon, Pigott, David M, Pilgrim, Thomas, Piracha, Zahra Zahid, Piradov, Michael A, Pirouzpanah, Saeed, Plakkal, Nishad, Plotnikov, Evgenii, Podder, Vivek, Poddighe, Dimitri, Polinder, Suzanne, Polkinghorne, Kevan R, Poluru, Ramesh, Ponkilainen, Ville T, Porru, Fabio, Postma, Maarten J, Poudel, Govinda Raj, Pourshams, Akram, Pourtaheri, Naeimeh, Prada, Sergio I, Pradhan, Pranil Man Singh, Prakasham, Thejeswar N, Prasad, Manya, Prashant, Akila, Prates, Elton Junio Sady, Prieto Alhambra, Daniel, PRISCILLA, TINA, Pritchett, Natalie, Purohit, Bharathi M, Puvvula, Jagadeesh, Qasim, Nameer Hashim, Qattea, Ibrahim, Qazi, Asma Saleem, Qian, Gangzhen, Qiu, Suli, Qureshi, Maryam Faiz, Rabiee Rad, Mehrdad, Radfar, Amir, Radhakrishnan, Raghu Anekal, Radhakrishnan, Venkatraman, Raeisi Shahraki, Hadi, Rafferty, Quinn, Raggi, Alberto, Raghav, Pankaja Raghav, Raheem, Nasiru, Rahim, Fakher, Rahim, Md Jillur, Rahimi-Movaghar, Vafa, Rahman, Md Mosfequr, Rahman, Mohammad Hifz Ur, Rahman, Mosiur, Rahman, Muhammad Aziz, Rahmani, Amir Masoud, Rahmani, Shayan, Rahmanian, Vahid, Rajaa, Sathish, Rajput, Prashant, Rakovac, Ivo, Ramasamy, Shakthi Kumaran, Ramazanu, Sheena, Rana, Kritika, Ranabhat, Chhabi Lal, Rancic, Nemanja, Rane, Amey, Rao, Chythra R, Rao, Indu Ramachandra, Rao, Mithun, Rao, Sowmya J, Rasali, Drona Prakash, Rasella, Davide, Rashedi, Sina, Rashedi, Vahid, Rashidi, Mohammad-Mahdi, Rasouli-Saravani, Ashkan, Rasul, Azad, Rathnaiah Babu, Giridhara, Rauniyar, Santosh Kumar, Ravangard, Ramin, Ravikumar, Nakul, Rawaf, David Laith, Rawaf, Salman, Rawal, Lal, Rawassizadeh, Reza, Rawlley, Bharat, Raza, Rabail Zehra, Razo, Christian, Redwan, Elrashdy Moustafa Mohamed, Rehman, Faizan Ur, Reifels, Lennart, Reiner Jr, Robert C, Remuzzi, Giuseppe, Reyes, Luis Felipe, Rezaei, Maryam, Rezaei, Nazila, Rezaei, Negar, Rezaeian, Mohsen, Rhee, Taeho Gregory, Riaz, Mavra A, Ribeiro, Antonio Luiz P, Rickard, Jennifer, Riva, Hannah R, Robinson-Oden, Hannah Elizabeth, Rodrigues, Célia Fortuna, Rodrigues, Mónica, Roever, Leonardo, Rogowski, Emma Lynn Best, Rohloff, Peter, Romadlon, Debby Syahru, Romero-Rodríguez, Esperanza, Romoli, Michele, Ronfani, Luca, Roshandel, Gholamreza, Roth, Gregory A, Rout, Himanshu Sekhar, Roy, Nitai, Roy, Priyanka, Rubagotti, Enrico, Ruela, Guilherme de Andrade, Rumisha, Susan Fred, Runghien, Tilleye, Rwegerera, Godfrey M, Rynkiewicz, Andrzej, S N, Chandan, Saad, Aly M A, Saadatian, Zahra, Saber, Korosh, Saber-Ayad, Maha Mohamed, SaberiKamarposhti, Morteza, Sabour, Siamak, Sacco, Simona, Sachdev, Perminder S, Sachdeva, Rajesh, Saddik, Basema, Saddler, Adam, Sadee, Bashdar Abuzed, Sadeghi, Ehsan, Sadeghi, Erfan, Sadeghian, Farideh, Saeb, Mohammad Reza, Saeed, Umar, Safaeinejad, Fahimeh, Safi, Sher Zaman, Sagar, Rajesh, Saghazadeh, Amene, Sagoe, Dominic, Saheb Sharif-Askari, Fatemeh, Saheb Sharif-Askari, Narjes, Sahebkar, Amirhossein, Sahoo, Soumya Swaroop, Sahoo, Umakanta, Sahu, Monalisha, Saif, Zahra, Sajid, Mirza Rizwan, Sakshaug, Joseph W, Salam, Nasir, Salamati, Payman, Salami, Afeez Abolarinwa, Salaroli, Luciane B, Saleh, Mohamed A, Salehi, Sana, Salem, Marwa Rashad, Salem, Mohammed Z Y, Salimi, Sohrab, Samadi Kafil, Hossein, Samadzadeh, Sara, Samargandy, Saad, Samodra, Yoseph Leonardo, Samy, Abdallah M, Sanabria, Juan, Sanna, Francesca, Santomauro, Damian Francesco, Santos, Itamar S, Santric-Milicevic, Milena M, Sao Jose, Bruno Piassi, Sarasmita, Made Ary, Saraswathy, Sivan Yegnanarayana Iyer, Saravanan, Aswini, Saravi, Babak, Sarikhani, Yaser, Sarkar, Tanmay, Sarmiento-Suárez, Rodrigo, Sarode, Gargi Sachin, Sarode, Sachin C, Sarveazad, Arash, Sathian, Brijesh, Sathish, Thirunavukkarasu, Satpathy, Maheswar, Sayeed, Abu, Sayeed, Md Abu, Saylan, Mete, Sayyah, Mehdi, Scarmeas, Nikolaos, Schaarschmidt, Benedikt Michael, Schlaich, Markus P, Schlee, Winfried, Schmidt, Maria Inês, Schneider, Ione Jayce Ceola, Schuermans, Art, Schumacher, Austin E, Schutte, Aletta Elisabeth, Schwarzinger, Michaël, Schwebel, David C, Schwendicke, Falk, Šekerija, Mario, Selvaraj, Siddharthan, Senapati, Sabyasachi, Senthilkumaran, Subramanian, Sepanlou, Sadaf G, Serban, Dragos, Sethi, Yashendra, Sha, Feng, Shabany, Maryam, Shafaat, Amir, Shafie, Mahan, Shah, Nilay S, Shah, Pritik A, Shah, Syed Mahboob, Shahabi, Saeed, Shahbandi, Ataollah, Shahid, Izza, Shahid, Samiah, Shahid, Wajeehah, Shahsavari, Hamid R, Shahwan, Moyad Jamal, Shaikh, Ahmed, Shaikh, Masood Ali, Shakeri, Alireza, Shalash, Ali S, Sham, Sunder, Shamim, Muhammad Aaqib, Shams-Beyranvand, Mehran, Shamshad, Hina, Shamsi, Mohammad Anas, Shanawaz, Mohd, Shankar, Abhishek, Sharfaei, Sadaf, Sharifan, Amin, Sharifi-Rad, Javad, Sharma, Rajesh, Sharma, Saurab, Sharma, Ujjawal, Sharma, Vishal, Shastry, Rajesh P, Shavandi, Amin, Shayan, Maryam, Shehabeldine, Amr Mohamed Elsayed, Sheikh, Aziz, Sheikhi, Rahim Ali, Shen, Jiabin, Shetty, Adithi, Shetty, B Suresh Kumar, Shetty, Pavanchand H, Shi, Peilin, Shibuya, Kenji, Shiferaw, Desalegn, Shigematsu, Mika, Shin, Min-Jeong, Shin, Youn Ho, Shiri, Rahman, Shirkoohi, Reza, Shitaye, Nebiyu Aniley, Shittu, Aminu, Shiue, Ivy, Shivakumar, K M, Shivarov, Velizar, Shokraneh, Farhad, Shokri, Azad, Shool, Sina, Shorofi, Seyed Afshin, Shrestha, Sunil, Shuval, Kerem, Siddig, Emmanuel Edwar, Silva, João Pedro, Silva, Luís Manuel Lopes Rodrigues, Silva, Soraia, Simpson, Colin R, Singal, Anjali, Singh, Abhinav, Singh, Balbir Bagicha, Singh, Garima, Singh, Jasbir, Singh, Narinder Pal, Singh, Paramdeep, Singh, Surjit, Sinha, Dhirendra Narain, Sinto, Robert, Siraj, Md Shahjahan, Sirota, Sarah Brooke, Sitas, Freddy, Sivakumar, Shravan, Skryabin, Valentin Yurievich, Skryabina, Anna Aleksandrovna, Sleet, David A, Socea, Bogdan, Sokhan, Anton, Solanki, Ranjan, Solanki, Shipra, Soleimani, Hamidreza, Soliman, Sameh S M, Song, Suhang, Song, Yimeng, Sorensen, Reed J D, Soriano, Joan B, Soyiri, Ireneous N, Spartalis, Michael, Spearman, Sandra, Sreeramareddy, Chandrashekhar T, Srivastava, Vijay Kumar, Stanaway, Jeffrey D, Stanikzai, Muhammad Haroon, Stark, Benjamin A, Starnes, Joseph R, Starodubova, Antonina V, Stein, Caroline, Stein, Dan J, Steinbeis, Fridolin, Steiner, Caitlyn, Steinmetz, Jaimie D, Steiropoulos, Paschalis, Stevanović, Aleksandar, Stockfelt, Leo, Stokes, Mark A, Stortecky, Stefan, Subramaniyan, Vetriselvan, Suleman, Muhammad, Suliankatchi Abdulkader, Rizwan, Sultana, Abida, Sun, Haitong Zhe, Sun, Jing, Sundström, Johan, Sunkersing, David, Sunnerhagen, Katharina S, Swain, Chandan Kumar, Szarpak, Lukasz, Szeto, Mindy D, Szócska, Miklós, Tabaee Damavandi, Payam, Tabarés-Seisdedos, Rafael, Tabatabaei, Seyyed Mohammad, Tabatabaei Malazy, Ozra, Tabatabaeizadeh, Seyed-Amir, Tabatabai, Shima, Tabish, Mohammad, TADAKAMADLA, JYOTHI, Tadakamadla, Santosh Kumar, Taheri Abkenar, Yasaman, Taheri Soodejani, Moslem, Taiba, Jabeen, Takahashi, Ken, Talaat, Iman M, Talukder, Ashis, Tampa, Mircea, Tamuzi, Jacques Lukenze, Tan, Ker-Kan, Tandukar, Sarmila, Tang, Haosu, Tang, Hong K, Tarigan, Ingan Ukur, Tariku, Mengistie Kassahun, Tariqujjaman, Md, Tarkang, Elvis Enowbeyang, Tavakoli Oliaee, Razieh, Tavangar, Seyed Mohammad, Taveira, Nuno, Tefera, Yibekal Manaye, Temsah, Mohamad-Hani, Temsah, Reem Mohamad Hani, Teramoto, Masayuki, Tesler, Riki, Teye-Kwadjo, Enoch, Thakur, Rishu, Thangaraju, Pugazhenthan, Thankappan, Kavumpurathu Raman, Tharwat, Samar, Thayakaran, Rasiah, Thomas, Nihal, Thomas, Nikhil Kenny, Thomson, Azalea M, Thrift, Amanda G, Thum, Chern Choong Chern, Thygesen, Lau Caspar, Tian, Jing, Tichopad, Ales, Ticoalu, Jansje Henny Vera, Tillawi, Tala, Tiruye, Tenaw Yimer, Titova, Mariya Vladimirovna, Tonelli, Marcello, Topor-Madry, Roman, Toriola, Adetunji T, Torre, Anna E, Touvier, Mathilde, Tovani-Palone, Marcos Roberto, Tran, Jasmine T, Tran, Nghia Minh, Trico, Domenico, Tromans, Samuel Joseph, Truyen, Thien Tan Tri Tai, Tsatsakis, Aristidis, Tsegay, Guesh Mebrahtom, Tsermpini, Evangelia Eirini, Tumurkhuu, Munkhtuya, Tung, Kang, Tyrovolas, Stefanos, Uddin, Sayed Mohammad Nazim, Udoakang, Aniefiok John, Udoh, Arit, Ullah, Atta, Ullah, Irfan, Ullah, Saeed, Ullah, Sana, Umakanthan, Srikanth, Umeokonkwo, Chukwuma David, Unim, Brigid, Unnikrishnan, Bhaskaran, Unsworth, Carolyn Anne, Upadhyay, Era, Urso, Daniele, Usman, Jibrin Sammani, Vahabi, Seyed Mohammad, Vaithinathan, Asokan Govindaraj, Valizadeh, Rohollah, Van de Velde, Sarah M, Van den Eynde, Jef, Varga, Orsolya, Vart, Priya, Varthya, Shoban Babu, Vasankari, Tommi Juhani, Vasic, Milena, Vaziri, Siavash, Vellingiri, Balachandar, Venketasubramanian, Narayanaswamy, Verghese, Nicholas Alexander, Verma, Madhur, Veroux, Massimiliano, Verras, Georgios-Ioannis, Vervoort, Dominique, Villafañe, Jorge Hugo, Villanueva, Gabriela Ines, Vinayak, Manish, Violante, Francesco S, Viskadourou, Maria, Vladimirov, Sergey Konstantinovitch, Vlassov, Vasily, Vo, Bay, Vollset, Stein Emil, Vongpradith, Avina, Vos, Theo, Vujcic, Isidora S, Vukovic, Rade, Wafa, Hatem A, Waheed, Yasir, Wamai, Richard G, Wang, Cong, Wang, Ning, Wang, Shu, Wang, Song, Wang, Yanzhong, Wang, Yuan-Pang, Waqas, Muhammad, Ward, Paul, Wassie, Emebet Gashaw, Watson, Stefanie, Watson, Stephanie Louise Watson, Weerakoon, Kosala Gayan, Wei, Melissa Y, Weintraub, Robert G, Weiss, Daniel J, Westerman, Ronny, Whisnant, Joanna L, Wiangkham, Taweewat, Wickramasinghe, Dakshitha Praneeth, Wickramasinghe, Nuwan Darshana, Wilandika, Angga, Wilkerson, Caroline, Willeit, Peter, Wilson, Shadrach, Wojewodzic, Marcin W, Woldegebreal, Demewoz H, Wolf, Axel Walter, Wolfe, Charles D A, Wondimagegene, Yohannes Addisu, Wong, Yen Jun, Wongsin, Utoomporn, Wu, Ai-Min, Wu, Chenkai, Wu, Felicia, Wu, Xinsheng, Wu, Zenghong, Xia, Juan, Xiao, Hong, Xie, Yang, Xu, Suowen, Xu, Wang-Dong, Xu, Xiaoyue, Xu, Yvonne Yiru, Yadollahpour, Ali, Yamagishi, Kazumasa, Yang, Danting, Yang, Lin, Yano, Yuichiro, Yao, Yao, Yaribeygi, Habib, Ye, Pengpeng, Yehualashet, Sisay Shewasinad, Yesiltepe, Metin, Yesuf, Subah Abderehim, Yezli, Saber, Yi, Siyan, Yigezu, Amanuel, Yiğit, Arzu, Yiğit, Vahit, Yip, Paul, Yismaw, Malede Berihun, Yismaw, Yazachew, Yon, Dong Keon, Yonemoto, Naohiro, Yoon, Seok-Jun, You, Yuyi, Younis, Mustafa Z, Yousefi, Zabihollah, Yu, Chuanhua, Yu, Yong, Yuh, Faith H, Zadey, Siddhesh, Zadnik, Vesna, Zafari, Nima, Zakham, Fathiah, Zaki, Nazar, Zaman, Sojib Bin, Zamora, Nelson, Zand, Ramin, Zangiabadian, Moein, Zar, Heather J, Zare, Iman, Zarrintan, Armin, Zeariya, Mohammed G M, Zeinali, Zahra, Zhang, Haijun, Zhang, Jianrong, Zhang, Jingya, Zhang, Liqun, Zhang, Yunquan, Zhang, Zhi-Jiang, Zhao, Hanqing, Zhong, Chenwen, Zhou, Juexiao, Zhu, Bin, Zhu, Lei, Ziafati, Makan, Zielińska, Magdalena, Zitoun, Osama A, Zoladl, Mohammad, Zou, Zhiyong, Zuhlke, Liesl J, Zumla, Alimuddin, Zweck, Elric, Zyoud, Samer H, Wool, Eve E, and Murray, Christopher J L

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2024
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34. Parameterized algorithms for locating-dominating sets

Author

Cappelle, Márcia R., Gomes, Guilherme C. M., and Santos, Vinicius F. dos

Subjects
Computer Science - Data Structures and Algorithms
Abstract

A locating-dominating set $D$ of a graph $G$ is a dominating set of $G$ where each vertex not in $D$ has a unique neighborhood in $D$, and the Locating-Dominating Set problem asks if $G$ contains such a dominating set of bounded size. This problem is known to be $\mathsf{NP-hard}$ even on restricted graph classes, such as interval graphs, split graphs, and planar bipartite subcubic graphs. On the other hand, it is known to be solvable in polynomial time for some graph classes, such as trees and, more generally, graphs of bounded cliquewidth. While these results have numerous implications on the parameterized complexity of the problem, little is known in terms of kernelization under structural parameterizations. In this work, we begin filling this gap in the literature. Our first result shows that Locating-Dominating Set, when parameterized by the solution size $d$, admits no $2^{o(d \log d)}$ time algorithm unless the Exponential Time Hypothesis fails; as a corollary, we also show that no $n^{o(d)}$ time algorithm exists under ETH, implying that the naive $\mathsf{XP}$ algorithm is essentially optimal. We present an exponential kernel for the distance to cluster parameterization and show that, unless $\mathsf{NP-hard} \subseteq \mathsf{NP-hard}/$\mathsf{poly}$, no polynomial kernel exists for Locating-Dominating Set when parameterized by vertex cover nor when parameterized by distance to clique. We then turn our attention to parameters not bounded by neither of the previous two, and exhibit a linear kernel when parameterizing by the max leaf number; in this context, we leave the parameterization by feedback edge set as the primary open problem in our study., Comment: 25 pages, 18 figures. Previous version appeared in the proceedings of LAGOS2021

Published
2020

35. On structural parameterizations of the selective coloring problem

Author

Gomes, Guilherme C. M. and Santos, Vinicius F. dos

Subjects
Computer Science - Data Structures and Algorithms
Abstract

In the Selective Coloring problem, we are given an integer $k$, a graph $G$, and a partition of $V(G)$ into $p$ parts, and the goal is to decide whether or not we can pick exactly one vertex of each part and obtain a $k$-colorable induced subgraph of $G$. This generalization of Vertex Coloring has only recently begun to be studied by Demange et al. [Theoretical Computer Science, 2014], motivated by scheduling problems on distributed systems, with Guo et al. [TAMC, 2020] discussing the first results on the parameterized complexity of the problem. In this work, we study multiple structural parameterizations for Selective Coloring. We begin by revisiting the many hardness results of Demange et al. and show how they may be used to provide intractability proofs for widely used parameters such as pathwidth, distance to co-cluster, and max leaf number. Afterwards, we present fixed-parameter tractability algorithms when parameterizing by distance to cluster, or under the joint parameterizations treewidth and number of parts, and co-treewidth and number of parts. Our main contribution is a proof that, for every fixed $k \geq 1$, Selective Coloring does not admit a polynomial kernel when jointly parameterized by the vertex cover number and the number of parts, which implies that Multicolored Independent Set does not admit a polynomial kernel under the same parameterization., Comment: 14 pages, 2 figures. Submitted to LAGOS2021

Published
2020

36. Unfolding selection to infer individual risk heterogeneity for optimising disease forecasts and policy development

Author

Gomes, M. Gabriela M., Feasey, Nicholas A., Ferreira, Marcelo U., LaCourse, E. James, Langwig, Kate E., Reimer, Lisa, Ringwald, Beate, Rylance, Jamie, Stothard, J. Russell, Taegtmeyer, Miriam, Terlouw, Dianne J., Tolhurst, Rachel, Wingfield, Tom, and Gordon, Stephen B.

Subjects
Quantitative Biology - Populations and Evolution, 92
Abstract

Mathematical models are increasing adopted for setting targets for disease prevention and control. As model-informed policies are implemented, however, the inaccuracies of some forecasts become apparent, for example overprediction of infection burdens and overestimation of intervention impacts. Here, we attribute these discrepancies to methodological limitations in capturing the heterogeneities of real-world systems. The mechanisms underpinning single factors for infection and their interactions determine individual propensities to acquire disease. These are potentially so numerous that to attain a full mechanistic description may be unfeasible. To contribute constructively to the development of health policies, model developers either leave factors out (reductionism) or adopt a broader but coarse description (holism). In our view, predictive capacity requires holistic descriptions of heterogeneity which are currently underutilised in infectious disease epidemiology but common in other disciplines., Comment: 10 pages, 3 figures

Published
2020

37. Herd immunity under individual variation and reinfection

Author

Montalbán, Antonio, Corder, Rodrigo M., and Gomes, M. Gabriela M.

Subjects
Quantitative Biology - Populations and Evolution, Physics - Physics and Society, 92D30
Abstract

We study a SEIR model considered by Gomes et al. \cite{Gomes2020} and Aguas et al. \cite{Aguas2020} where different individuals are assumed to have different levels of susceptibility or exposure to infection. Under this heterogeneity assumption, epidemic growth is effectively suppressed when the percentage of population having acquired immunity surpasses a critical level - the herd immunity threshold - that is lower than in homogeneous populations. We find explicit formulas to calculate herd immunity thresholds and stable configuration, and explore extensions of the model.

Published
2020

38. FPT and kernelization algorithms for the k-in-a-tree problem

Author

Gomes, Guilherme C. M., Santos, Vinicius F. dos, da Silva, Murilo V. G., and Szwarcfiter, Jayme L.

Subjects
Computer Science - Data Structures and Algorithms
Abstract

The three-in-a-tree problem asks for an induced tree of the input graph containing three mandatory vertices. In 2006, Chudnovsky and Seymour [Combinatorica, 2010] presented the first polynomial time algorithm for this problem, which has become a critical subroutine in many algorithms for detecting induced subgraphs, such as beetles, pyramids, thetas, and even and odd-holes. In 2007, Derhy and Picouleau [Discrete Applied Mathematics, 2009] considered the natural generalization to $k$ mandatory vertices, proving that, when $k$ is part of the input, the problem is $\mathsf{NP}$-complete, and ask what is the complexity of four-in-a-tree. Motivated by this question and the relevance of the original problem, we study the parameterized complexity of $k$-in-a-tree. We begin by showing that the problem is $\mathsf{W[1]}$-hard when jointly parameterized by the size of the solution and minimum clique cover and, under the Exponential Time Hypothesis, does not admit an $n^{o(k)}$ time algorithm. Afterwards, we use Courcelle's Theorem to prove fixed-parameter tractability under cliquewidth, which prompts our investigation into which parameterizations admit single exponential algorithms; we show that such algorithms exist for the unrelated parameterizations treewidth, distance to cluster, and distance to co-cluster. In terms of kernelization, we present a linear kernel under feedback edge set, and show that no polynomial kernel exists under vertex cover nor distance to clique unless $\mathsf{NP} \subseteq \mathsf{coNP}/\mathsf{poly}$. Along with other remarks and previous work, our tractability and kernelization results cover many of the most commonly employed parameters in the graph parameter hierarchy., Comment: 25 pages, 8 figures

Published
2020

39. Coloring Problems on Bipartite Graphs of Small Diameter

Author

Campos, Victor A., Gomes, Guilherme C. M., Ibiapina, Allen, Lopes, Raul, Sau, Ignasi, and Silva, Ana

Subjects
Mathematics - Combinatorics, Computer Science - Computational Complexity, Computer Science - Data Structures and Algorithms, 05C15, G.2.2, F.2.2
Abstract

We investigate a number of coloring problems restricted to bipartite graphs with bounded diameter. First, we investigate the $k$-List Coloring, List $k$-Coloring, and $k$-Precoloring Extension problems on bipartite graphs with diameter at most $d$, proving NP-completeness in most cases, and leaving open only the List $3$-Coloring and $3$-Precoloring Extension problems when $d=3$. Some of these results are obtained through a proof that the Surjective $C_6$-Homomorphism problem is NP-complete on bipartite graphs with diameter at most four. Although the latter result has been already proved [Vikas, 2017], we present ours as an alternative simpler one. As a byproduct, we also get that $3$-Biclique Partition is NP-complete. An attempt to prove this result was presented in [Fleischner, Mujuni, Paulusma, and Szeider, 2009], but there was a flaw in their proof, which we identify and discuss here. Finally, we prove that the $3$-Fall Coloring problem is NP-complete on bipartite graphs with diameter at most four, and prove that NP-completeness for diameter three would also imply NP-completeness of $3$-Precoloring Extension on diameter three, thus closing the previously mentioned open cases. This would also answer a question posed in [Kratochv\'il, Tuza, and Voigt, 2002]., Comment: 21 pages, 9 figures

Published
2020

40. Some results on Vertex Separator Reconfiguration

Author

Gomes, Guilherme C. M., Nogueira, Sérgio H., and Santos, Vinicius F. dos

Subjects
Computer Science - Computational Complexity, Computer Science - Data Structures and Algorithms
Abstract

We present the first results on the complexity of the reconfiguration of vertex separators under the three most popular rules: token addition/removal, token jumping, and token sliding. We show that, aside from some trivially negative instances, the first two rules are equivalent to each other and that, even if only on a subclass of bipartite graphs, TJ is not equivalent to the other two unless $\mathsf{NP} = \mathsf{PSPACE}$; we do this by showing a relationship between separators and independent sets in this subclass of bipartite graphs. In terms of polynomial time algorithms, we show that every class with a polynomially bounded number of minimal vertex separators admits an efficient algorithm under token jumping, then turn our attention to two classes that do not meet this condition: $\{3P_1, diamond\}$-free and series-parallel graphs. For the first, we describe a novel characterization, which we use to show that reconfiguring vertex separators under token jumping is always possible and that, under token sliding, it can be done in polynomial time; for series-parallel graphs, we also prove that reconfiguration is always possible under TJ and exhibit a polynomial time algorithm to construct the reconfiguration sequence., Comment: 21 pages, 8 figures

Published
2020

43. Lorentz-symmetry violating physics in a supersymmetric scenario in $(2+1)$-D

Author

Bernal, L. D., Gaete, Patricio, Gomes, Y. P. M., and Helayël-Neto, José A.

Subjects
High Energy Physics - Theory
Abstract

We study the dimensional reduction for a $(3+1)$-dimensional Lorentz Violating Lagrangian in the matter and gauge sectors in a Supersymmetric scenario. We thus obtain an effective model for photons induced by the effects of supersymmetry in our framework with Lorentz-symmetry violating. This model is discussed in connection with the attainment of a static potential between charged particles. Our calculation is done within the framework of the gauge-invariant, but path-dependent variable formalism. We thus find that the interaction energy displays a screening part, encoded by Bessel functions, and a linear confining potential., Comment: 7 pages

Published
2019
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44. Intersection graph of maximal stars

Author

Gomes, Guilherme C. M., Groshaus, Marina, Lima, Carlos V. G. C., and Santos, Vinicius F. dos

Subjects
Mathematics - Combinatorics, Computer Science - Discrete Mathematics
Abstract

A biclique of a graph $G$ is an induced complete bipartite subgraph of $G$ such that neither part is empty. A star is a biclique of $G$ such that one part has exactly one vertex. The star graph of $G$ is the intersection graph of the maximal stars of $G$. A graph $H$ is star-critical if its star graph is different from the star graph of any of its proper induced subgraphs. We begin by presenting a bound on the size of star-critical pre-images by a quadratic function on the number of vertices of the star graph, then proceed to describe a Krausz-type characterization for this graph class; we combine these results to show membership of the recognition problem in \textsf{NP}. We also present some properties of star graphs. In particular, we show that they are biconnected, that every edge belongs to at least one triangle, characterize the structures the pre-image must have in order to generate degree two vertices, and bound the diameter of the star graph with respect to the diameter of its pre-image. Finally, we prove a monotonicity theorem, which we apply to list every star graph on at most eight vertices., Comment: 22 pages, 13 figures

Published
2019

45. Structural Parameterizations for Equitable Coloring

Author

Gomes, Guilherme C. M., Guedes, Matheus R., and Santos, Vinicius F. dos

Subjects
Computer Science - Data Structures and Algorithms, Computer Science - Discrete Mathematics
Abstract

An $n$-vertex graph is equitably $k$-colorable if there is a proper coloring of its vertices such that each color is used either $\left\lfloor n/k \right\rfloor$ or $\left\lceil n/k \right\rceil$ times. While classic Vertex Coloring is fixed parameter tractable under well established parameters such as pathwidth and feedback vertex set, Equitable Coloring is $\mathsf{W}[1]$-$\mathsf{hard}$. We present an extensive study of structural parameterizations of Equitable Coloring, tackling both tractability and kernelization questions. We begin by showing that the problem is fixed parameter tractable when parameterized by distance to cluster or by distance to co-cluster -- improving on the $\mathsf{FPT}$ algorithm of Fiala et al. [Theoretical Computer Science, 2011] parameterized by vertex cover -- and also when parameterized by distance to disjoint paths of bounded length. To justify the latter result, we adapt a proof of Fellows et al. [Information and Computation, 2011] to show that Equitable Coloring is $\mathsf{W}[1]$-$\mathsf{hard}$ when simultaneously parameterized by distance to disjoint paths and number of colors. In terms of kernelization, on the positive side we present a linear kernel for the distance to clique parameter and a cubic kernel when parameterized by the maximum leaf number; on the other hand, we show that, unlike Vertex Coloring, Equitable Coloring does not admit a polynomial kernel when jointly parameterized by vertex cover and number of colors, unless $\mathsf{NP} \subseteq \mathsf{coNP}/\mathsf{poly}$. We also revisit the literature and derive other results on the parameterized complexity of the problem through minor reductions or other observations., Comment: 34 pages, 7 figures. Partial results were published in the proceedings of LATIN2020

Published
2019

46. Finding cuts of bounded degree: complexity, FPT and exact algorithms, and kernelization

Author

Gomes, Guilherme C. M. and Sau, Ignasi

Subjects
Computer Science - Data Structures and Algorithms, Computer Science - Computational Complexity, 05C15, G.2.2, F.2.2
Abstract

A matching cut is a partition of the vertex set of a graph into two sets $A$ and $B$ such that each vertex has at most one neighbor in the other side of the cut. The MATCHING CUT problem asks whether a graph has a matching cut, and has been intensively studied in the literature. Motivated by a question posed by Komusiewicz et al. [IPEC 2018], we introduce a natural generalization of this problem, which we call $d$-CUT: for a positive integer $d$, a $d$-cut is a bipartition of the vertex set of a graph into two sets $A$ and $B$ such that each vertex has at most $d$ neighbors across the cut. We generalize (and in some cases, improve) a number of results for the MATCHING CUT problem. Namely, we begin with an NP-hardness reduction for $d$-CUT on $(2d+2)$-regular graphs and a polynomial algorithm for graphs of maximum degree at most $d+2$. The degree bound in the hardness result is unlikely to be improved, as it would disprove a long-standing conjecture in the context of internal partitions. We then give FPT algorithms for several parameters: the maximum number of edges crossing the cut, treewidth, distance to cluster, and distance to co-cluster. In particular, the treewidth algorithm improves upon the running time of the best known algorithm for MATCHING CUT. Our main technical contribution, building on the techniques of Komusiewicz et al. [IPEC 2018], is a polynomial kernel for $d$-CUT for every positive integer $d$, parameterized by the distance to a cluster graph. We also rule out the existence of polynomial kernels when parameterizing simultaneously by the number of edges crossing the cut, the treewidth, and the maximum degree. Finally, we provide an exact exponential algorithm slightly faster than the naive brute force approach running in time $O^*(2^n)$., Comment: 24 pages, 8 figures

Published
2019

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