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We consider a natural generalization of chordal graphs, in which every minimal separator induces a subgraph with independence number at most $2$. Such graphs can be equivalently defined as graphs that do not contain the complete bipartite graph $K_{2,3}$ as an induced minor, that is, graphs from which $K_{2,3}$ cannot be obtained by a sequence of edge contractions and vertex deletions. We develop a polynomial-time algorithm for recognizing these graphs. Our algorithm relies on a characterization of $K_{2,3}$-induced minor-free graphs in terms of excluding particular induced subgraphs, called Truemper configurations., Comment: 18 pages

Community detection is a powerful tool from complex networks analysis that finds applications in various research areas. Several image segmentation methods rely for instance on community detection algorithms as a black box in order to compute undersegmentations, i.e. a small number of regions that represent areas of interest of the image. However, to the best of our knowledge, the efficiency of such an approach w.r.t. superpixels, that aim at representing the image at a smaller level while preserving as much as possible original information, has been neglected so far. The only related work seems to be the one by Liu et. al. (IET Image Processing, 2022) that developed a superpixels algorithm using a so-called modularity maximization approach, leading to relevant results. We follow this line of research by studying the efficiency of superpixels computed by state-of-the-art community detection algorithms on a 4-connected pixel graph, so-called pixel-grid. We first detect communities on such a graph and then apply a simple merging procedure that allows to obtain the desired number of superpixels. As we shall see, such methods result in the computation of relevant superpixels as emphasized by both qualitative and quantitative experiments, according to different widely-used metrics based on ground-truth comparison or on superpixels only. We observe that the choice of the community detection algorithm has a great impact on the number of communities and hence on the merging procedure. Similarly, small variations on the pixel-grid may provide different results from both qualitative and quantitative viewpoints. For the sake of completeness, we compare our results with those of several state-of-the-art superpixels algorithms as computed by Stutz et al. (Computer Vision and Image Understanding, 2018).

In the Trivially Perfect Editing problem one is given an undirected graph $G = (V,E)$ and an integer $k$ and seeks to add or delete at most $k$ edges in $G$ to obtain a trivially perfect graph. In a recent work, Dumas, Perez and Todinca [Algorithmica 2023] proved that this problem admits a kernel with $O(k^3)$ vertices. This result heavily relies on the fact that the size of trivially perfect modules can be bounded by $O(k^2)$ as shown by Drange and Pilipczuk [Algorithmica 2018]. To obtain their cubic vertex-kernel, Dumas, Perez and Todinca [Algorithmica 2023] then showed that a more intricate structure, so-called \emph{comb}, can be reduced to $O(k^2)$ vertices. In this work we show that the bound can be improved to $O(k)$ for both aforementioned structures and thus obtain a kernel with $O(k^2)$ vertices. Our approach relies on the straightforward yet powerful observation that any large enough structure contains unaffected vertices whose neighborhood remains unchanged by an editing of size $k$, implying strong structural properties.

The transport of aerosol discharge in the form of a passive scalar or tracer discharged from a single cough of a patient in a ventilated mock hospital isolation room is investigated via computational fluid dynamics (CFD). Healthcare worker (HCW) exposure to the aerosol is assessed through residence time analysis of the aerosol transported through the imperfect mixing conditions in the room. Flow features responsible for imperfect mixing, including short-circuiting or channeling between the patient and exhaust air vent (which leads to rapid expulsion of aerosols from the room), dead zones or re-circulation flow regions in the room, and the turbulent diffusion or spreading of aerosol across the room, are shown to play important factors determining the HCW exposure to the aerosol. The importance of each of these factors varies depending on the ventilation rate (ACH) and the placement of the exhaust air vent relative to the patient. For example, reducing ACH from 12 to 6 diminishes the importance of these flow features and the aerosol transport may be approximately modeled through the classical perfectly mixed assumption. At ACH = 12, especially when the ceiling exhaust is placed above the patient and the HCW, short-circuiting is the dominant feature in determining HCW exposure. But when the ceiling exhaust is placed away from the patient and HCW, the short-circuiting is weakened and the influence of dead zones, which trap aerosol, and turbulent diffusion, which allow the aerosol to escape, becomes more important. It is shown that the importance of these flow features and the resulting impact on HCW exposure can be quantified in terms of residence time distribution (RTD) metrics such as mean residence time and cumulative RTD. The results suggest that residence time analysis is a useful technique to be employed when designing a hospital isolation room and assessing HCW exposure to aerosols., Comment: 37 pages, Under review in the Journal of Occupational and Environmental Hygiene

We show that if the edges or vertices of an undirected graph $G$ can be covered by $k$ shortest paths, then the pathwidth of $G$ is upper-bounded by a single-exponential function of $k$. As a corollary, we prove that the problem Isometric Path Cover with Terminals (which, given a graph $G$ and a set of $k$ pairs of vertices called terminals, asks whether $G$ can be covered by $k$ shortest paths, each joining a pair of terminals) is FPT with respect to the number of terminals. The same holds for the similar problem Strong Geodetic Set with Terminals (which, given a graph $G$ and a set of $k$ terminals, asks whether there exist $\binom{k}{2}$ shortest paths covering $G$, each joining a distinct pair of terminals). Moreover, this implies that the related problems Isometric Path Cover and Strong Geodetic Set (defined similarly but where the set of terminals is not part of the input) are in XP with respect to parameter $k$.

We consider edge modification problems towards block and strictly chordal graphs, where one is given an undirected graph $G = (V,E)$ and an integer $k \in \mathbb{N}$ and seeks to edit (add or delete) at most $k$ edges from $G$ to obtain a block graph or a strictly chordal graph. The completion and deletion variants of these problems are defined similarly by only allowing edge additions for the former and only edge deletions for the latter. Block graphs are a well-studied class of graphs and admit several characterizations, e.g. they are diamond-free chordal graphs. Strictly chordal graphs, also referred to as block duplicate graphs, are a natural generalization of block graphs where one can add true twins of cut-vertices. Strictly chordal graphs are exactly dart and gem-free chordal graphs. We prove the NP-completeness for most variants of these problems and provide $O(k^2)$ vertex-kernels for Block Graph Edition and Block Graph Deletion, $O(k^3)$ vertex-kernels for Strictly Chordal Completion and Strictly Chordal Deletion and a $O(k^4)$ vertex-kernel for Strictly Chordal Edition.

We consider the Trivially Perfect Editing problem, where one is given an undirected graph $G = (V,E)$ and a parameter $k \in \mathbb{N}$ and seeks to edit (add or delete) at most $k$ edges from $G$ to obtain a trivially perfect graph. The related Trivially Perfect Completion and Trivially Perfect Deletion problems are obtained by only allowing edge additions or edge deletions, respectively. Trivially perfect graphs are both chordal and cographs, and have applications related to the tree-depth width parameter and to social network analysis. All variants of the problem are known to be NP-Complete and to admit so-called polynomial kernels. More precisely, the existence of an $O(k^3)$ vertex-kernel for Trivially Perfect Completion was announced by Guo (ISAAC 2007) but without a stand-alone proof. More recently, Drange and Pilipczuk (Algorithmica 2018) provided $O(k^7)$ vertex-kernels for these problems and left open the existence of cubic vertex-kernels. In this work, we answer positively to this question for all three variants of the problem.

We study the complexity of the two dual covering and packing distance-based problems Broadcast Domination and Multipacking in digraphs. A dominating broadcast of a digraph $D$ is a function $f:V(D)\to\mathbb{N}$ such that for each vertex $v$ of $D$, there exists a vertex $t$ with $f(t)>0$ having a directed path to $v$ of length at most $f(t)$. The cost of $f$ is the sum of $f(v)$ over all vertices $v$. A multipacking is a set $S$ of vertices of $D$ such that for each vertex $v$ of $D$ and for every integer $d$, there are at most $d$ vertices from $S$ within directed distance at most $d$ from $v$. The maximum size of a multipacking of $D$ is a lower bound to the minimum cost of a dominating broadcast of $D$. Let Broadcast Domination denote the problem of deciding whether a given digraph $D$ has a dominating broadcast of cost at most $k$, and Multipacking the problem of deciding whether $D$ has a multipacking of size at least $k$. It is known that Broadcast Domination is polynomial-time solvable for the class of all undirected graphs (that is, symmetric digraphs), while polynomial-time algorithms for Multipacking are known only for a few classes of undirected graphs. We prove that Broadcast Domination and Multipacking are both NP-complete for digraphs, even for planar layered acyclic digraphs of small maximum degree. Moreover, when parameterized by the solution cost/solution size, we show that the problems are W-hard. We also show that Broadcast Domination is FPT on acyclic digraphs, and that it does not admit a polynomial kernel for such inputs, unless the polynomial hierarchy collapses to its third level. In addition, we show that both problems are FPT when parameterized by the solution cost/solution size together with the maximum out-degree, and as well, by the vertex cover number. Finally, we give for both problems polynomial-time algorithms for some subclasses of acyclic digraphs., Comment: Extended abstract to appear in proceedings of IWOCA 2020

Obtaining reliable data describing local poverty metrics at a granularity that is informative to policy-makers requires expensive and logistically difficult surveys, particularly in the developing world. Not surprisingly, the poverty stricken regions are also the ones which have a high probability of being a war zone, have poor infrastructure and sometimes have governments that do not cooperate with internationally funded development efforts. We train a CNN on free and publicly available daytime satellite images of the African continent from Landsat 7 to build a model for predicting local economic livelihoods. Only 5% of the satellite images can be associated with labels (which are obtained from DHS Surveys) and thus a semi-supervised approach using a GAN (similar to the approach of Salimans, et al. (2016)), albeit with a more stable-to-train flavor of GANs called the Wasserstein GAN regularized with gradient penalty(Gulrajani, et al. (2017)) is used. The method of multitask learning is employed to regularize the network and also create an end-to-end model for the prediction of multiple poverty metrics., Comment: This project was recognized as the best two-person project during the Spring 2017 offering of CS 231N Convolutional Neural Networks for Visual Recognition. Second revised version corrects typographical errors and adds a few additional references

Obtaining detailed and reliable data about local economic livelihoods in developing countries is expensive, and data are consequently scarce. Previous work has shown that it is possible to measure local-level economic livelihoods using high-resolution satellite imagery. However, such imagery is relatively expensive to acquire, often not updated frequently, and is mainly available for recent years. We train CNN models on free and publicly available multispectral daytime satellite images of the African continent from the Landsat 7 satellite, which has collected imagery with global coverage for almost two decades. We show that despite these images' lower resolution, we can achieve accuracies that exceed previous benchmarks., Comment: Presented at NIPS 2017 Workshop on Machine Learning for the Developing World

In the context of Twitter, social capitalists are specific users trying to increase their number of followers and interactions by any means. These users are not healthy for the service, because they are either spammers or real users flawing the notions of influence and visibility. Studying their behavior and understanding their position in Twit-ter is thus of important interest. It is also necessary to analyze how these methods effectively affect user visibility. Based on a recently proposed method allowing to identify social capitalists, we tackle both points by studying how they are organized, and how their links spread across the Twitter follower-followee network. To that aim, we consider their position in the network w.r.t. its community structure. We use the concept of community role of a node, which describes its position in a network depending on its connectiv-ity at the community level. However, the topological measures originally defined to characterize these roles consider only certain aspects of the community-related connectivity, and rely on a set of empirically fixed thresholds. We first show the limitations of these measures, before extending and generalizing them. Moreover, we use an unsupervised approach to identify the roles, in order to provide more flexibility relatively to the studied system. We then apply our method to the case of social capitalists and show they are highly visible on Twitter, due to the specific roles they hold., Comment: arXiv admin note: substantial text overlap with arXiv:1406.6611

In the context of Twitter, social capitalists are specific users trying to increase their number of followers and interactions by any means. These users are not healthy for the Twitter network since they flaw notions of influence and visibility. Indeed, it has recently been observed that they are real and active users that can help malicious users such as spammers gaining influence. Studying their behavior and understanding their position in Twitter is thus of important interest. A recent work provided an efficient way to detect social capitalists using two simple topological measures. Based on this detection method, we study how social capitalists are distributed over Twitter's friend-to-follower network. We are especially interested in analyzing how they are organized, and how their links spread across the network. Answering these questions allows to know whether the social capitalism methods increase the actual visibility on the service. To that aim, we study the position of social capitalists on Twitter w.r.t. the community structure of the network. We base our work on the concept of community role of a node, which describes its position in a network depending on its connectivity at the community level. The topological measures originally defined to characterize these roles consider only some aspects of community-related connectivity and rely on a set of empirically fixed thresholds. We first show the limitations of such measures and then extend and generalize them by considering new aspects of the community-related connectivity. Moreover, we use an unsupervised approach to distinguish the roles, in order to provide more flexibility relatively to the studied system. We then apply our method to the case of social capitalists and show that they are highly visible on Twitter, due to the specific roles they occupy., Comment: IEEE/ACM International Conference on Advances in Social Network Analysis and Mining (ASONAM), P\'ekin : China (2014)

The notion of community structure is particularly useful when analyzing complex networks, because it provides an intermediate level, compared to the more classic global (whole network) and local (node neighborhood) approaches. The concept of community role of a node was derived from this base, in order to describe the position of a node in a network depending on its connectivity at the community level. However, the existing approaches are restricted to undirected networks, use topological measures which do not consider all aspects of community-related connectivity, and their role identification methods are not generalizable to all networks. We tackle these limitations by generalizing and extending the measures, and using an unsupervised approach to determine the roles. We then illustrate the applicability of our method by analyzing a Twitter network.We show how our modifications allow discovering the fact some particular users called social capitalists occupy very specific roles in this system. --- La notion de structure de communaut\'es est particuli\`erement utile pour \'etudier les r\'eseaux complexes, car elle am\`ene un niveau d'analyse interm\'ediaire, par opposition aux plus classiques niveaux local (voisinage des noeuds) et global (r\'eseau entier). Le concept de r\^ole communautaire permet de d\'ecrire le positionnement d'un noeud en fonction de sa connectivit\'e communautaire. Cependant, les approches existantes sont restreintes aux r\'eseaux non-orient\'es, utilisent des mesures topologiques ne consid\'erant pas tous les aspects de la connectivit\'e communautaire, et des m\'ethodes d'identification des r\^oles non-g\'en\'eralisables \`a tous les r\'eseaux. Nous proposons de r\'esoudre ces probl\`emes en g\'en\'eralisant les mesures existantes, et en utilisant une m\'ethode non-supervis\'ee pour d\'eterminer les r\^oles. Nous illustrons l'int\'er\^et de notre m\'ethode en l'appliquant au r\'eseau de Twitter. Nous montrons que nos modifications mettent en \'evidence les r\^oles sp\'ecifiques d'utilisateurs particuliers du r\'eseau, nomm\'es capitalistes sociaux., Comment: arXiv admin note: substantial text overlap with arXiv:1309.2132

Les capitalistes sociaux sont des utilisateurs de m\'edias sociaux tels que Twitter, appliquant diverses techniques pour obtenir un maximum de visibilit\'e. Ils peuvent \^etre n\'efastes \`a l'\'equilibre du service, dans la mesure o\`u leurs comptes, en gagnant en importance sans r\'eelle raison de contenu, rendent difficile l'acc\`es \`a un contenu pertinent. Dans ce travail, nous nous int\'eressons \`a leur caract\'erisation d'un point de vue purement topologique, i.e. sans consid\'erer la nature des contenus partag\'es. Nous utilisons pour cela la notion de r\^ole communautaire, qui est bas\'ee sur la structure de communaut\'es du r\'eseau \'etudi\'e. Nous apportons des modifications \`a des mesures pr\'ec\'edemment d\'efinies \`a cet effet, et proposons une m\'ethode objective de d\'etection des r\^oles. Nous appliquons ensuite notre m\'ethode \`a l'analyse d'un r\'eseau repr\'esentant Twitter. Nos r\'esultats montrent que les r\^oles que nous identifions via nos mesures se r\'ev\`elent particuli\`erement coh\'erents par rapport aux capitalistes sociaux du r\'eseau Twitter, dont le comportement est clairement identifi\'e---Social capitalists are social media users taking advantage of various methods to maximize their visibility. This results in artificially important accounts, in the sense this importance is not backed by any real content. The risk is then to see those accounts hiding relevant contents and therefore preventing other users to access them. In this work, we want to characterize social capitalists from a purely topological perspective, i.e. without considering the nature of the shared contents. For this purpose, we use the notion of community role, based on the community structure of the studied network. We modify some measures previously designed for this matter, and propose an objective method to determine roles. We then apply this method to the analysis of a Twitter network. Our results show the roles identified through our measures are particularly consistent with Twitter's social capitalists, whose behavior was clearly identified.

A Ranking r-Constraint Satisfaction Problem (ranking r-CSP) consists of a ground set of vertices V, an arity r >= 2, a parameter k and a constraint system c, where c is a function which maps rankings of r-sized subsets of V to {0,1}. The objective is to decide if there exists a ranking of the vertices satisfying all but at most k constraints. Famous ranking r-CSP include the Feedback Arc Set in Tournaments and Betweenness in Tournaments problems. We consider these problems from the kernelization viewpoint. We prove that so-called l_r-simply characterized ranking r-CSPs admit linear vertex-kernels whenever they admit constant-factor approximation algorithms. This implies that r-Betweenness in Tournaments and r-Transitive Feedback Arc Set In Tournaments, two natural generalizations of the previously mentioned problems, admit linear vertex-kernels. Moreover, we introduce another generalization of Feedback Arc Set in Tournaments, which does not fit the aforementioned framework. We obtain a 5-approximation and a linear vertex-kernel for this problem., Comment: Several flaws (Lemma 2.17) appeared in the previous version; this version corrects them

Given a graph G = (V,E) and a positive integer k, the Proper Interval Completion problem asks whether there exists a set F of at most k pairs of (V \times V)\E such that the graph H = (V,E \cup F) is a proper interval graph. The Proper Interval Completion problem finds applications in molecular biology and genomic research. First announced by Kaplan, Tarjan and Shamir in FOCS '94, this problem is known to be FPT, but no polynomial kernel was known to exist. We settle this question by proving that Proper Interval Completion admits a kernel with at most O(k^5) vertices. Moreover, we prove that a related problem, the so-called Bipartite Chain Deletion problem, admits a kernel with at most O(k^2) vertices, completing a previous result of Guo.

We develop a technique that we call Conflict Packing in the context of kernelization, obtaining (and improving) several polynomial kernels for editing problems on dense instances. We apply this technique on several well-studied problems: Feedback Arc Set in (Bipartite) Tournaments, Dense Rooted Triplet Inconsistency and Betweenness in Tournaments. For the former, one is given a (bipartite) tournament $T = (V,A)$ and seeks a set of at most $k$ arcs whose reversal in $T$ results in an acyclic (bipartite) tournament. While a linear vertex-kernel is already known for the first problem, using the Conflict Packing allows us to find a so-called safe partition, the central tool of the kernelization algorithm in, with simpler arguments. For the case of bipartite tournaments, the same technique allows us to obtain a quadratic vertex-kernel. Again, such a kernel was already known to exist, using the concept of so-called bimodules. We believe however that providing an unifying technique to cope with such problems is interesting. Regarding Dense Rooted Triplet Inconsistency, one is given a set of vertices $V$ and a dense collection $\mathcal{R}$ of rooted binary trees over three vertices of $V$ and seeks a rooted tree over $V$ containing all but at most $k$ triplets from $\mathcal{R}$. As a main consequence of our technique, we prove that the Dense Rooted Triplet Inconsistency problem admits a linear vertex-kernel. This result improves the best known bound of $O(k^2)$ vertices for this problem. Finally, we use this technique to obtain a linear vertex-kernel for Betweenness in Tournaments, where one is given a set of vertices $V$ and a dense collection $\mathcal{R}$ of so-called betweenness triplets and seeks a linear ordering of the vertices containing all but at most $k$ triplets from $\mathcal{R}$.

Given a graph G = (V,E) and an integer k, an edge modification problem for a graph property P consists in deciding whether there exists a set of edges F of size at most k such that the graph H = (V,E \vartriangle F) satisfies the property P. In the P edge-completion problem, the set F of edges is constrained to be disjoint from E; in the P edge-deletion problem, F is a subset of E; no constraint is imposed on F in the P edge-edition problem. A number of optimization problems can be expressed in terms of graph modification problems which have been extensively studied in the context of parameterized complexity. When parameterized by the size k of the edge set F, it has been proved that if P is an hereditary property characterized by a finite set of forbidden induced subgraphs, then the three P edge-modification problems are FPT. It was then natural to ask whether these problems also admit a polynomial size kernel. Using recent lower bound techniques, Kratsch and Wahlstrom answered this question negatively. However, the problem remains open on many natural graph classes characterized by forbidden induced subgraphs. Kratsch and Wahlstrom asked whether the result holds when the forbidden subgraphs are paths or cycles and pointed out that the problem is already open in the case of P4-free graphs (i.e. cographs). This paper provides positive and negative results in that line of research. We prove that parameterized cograph edge modification problems have cubic vertex kernels whereas polynomial kernels are unlikely to exist for the Pl-free and Cl-free edge-deletion problems for large enough l.

A tournament T=(V,A) is a directed graph in which there is exactly one arc between every pair of distinct vertices. Given a digraph on n vertices and an integer parameter k, the Feedback Arc Set problem asks whether the given digraph has a set of k arcs whose removal results in an acyclic digraph. The Feedback Arc Set problem restricted to tournaments is known as the k-Feedback Arc Set in Tournaments (k-FAST) problem. In this paper we obtain a linear vertex kernel for k-FAST. That is, we give a polynomial time algorithm which given an input instance T to k-FAST obtains an equivalent instance T' on O(k) vertices. In fact, given any fixed e>0, the kernelized instance has at most (2+e)k vertices. Our result improves the previous known bound of O(k^2) on the kernel size for k-FAST. Our kernelization algorithm solves the problem on a subclass of tournaments in polynomial time and uses a known polynomial time approximation scheme for k-FAST.

A graph G=(V,E) is a 3-leaf power iff there exists a tree T whose leaves are V and such that (u,v) is an edge iff u and v are at distance at most 3 in T. The 3-leaf power graph edge modification problems, i.e. edition (also known as the closest 3-leaf power), completion and edge-deletion, are FTP when parameterized by the size of the edge set modification. However polynomial kernel was known for none of these three problems. For each of them, we provide cubic kernels that can be computed in linear time for each of these problems. We thereby answer an open problem first mentioned by Dom, Guo, Huffner and Niedermeier (2005)., Comment: Submitted