Search

This document discusses the importance of optimization in various fields such as statistics, biology, finance, economics, and control. It highlights the advancements made in optimization theory and methods, including first-order methods and augmented Lagrangian methods. The document also introduces a special issue on "Symmetry in Optimization Theory, Algorithms and Applications," which features five papers on topics such as ensemble learning, ant colony system algorithms, subspace algorithms, consensus problems in multi-agent systems, and dynamic conditional correlation models. The authors express their gratitude to the contributors and reviewers of the special issue. [Extracted from the article]

A k-page upward book embedding (kUBE) of a directed acyclic graph G is a book embeddings of G on k pages with the additional requirement that the vertices appear in a topological ordering along the spine of the book. The kUBE Testing problem, which asks whether a graph admits a kUBE, was introduced in 1999 by Heath, Pemmaraju, and Trenk (SIAM J Comput 28(4), 1999). In a companion paper, Heath and Pemmaraju (SIAM J Comput 28(5), 1999) proved that the problem is linear-time solvable for k = 1 and NP-complete for k = 6 . Closing this gap has been a central question in algorithmic graph theory since then. In this paper, we make a major contribution towards a definitive answer to the above question by showing that kUBE Testing is NP-complete for k ≥ 3 , even for st-graphs, i.e., acyclic directed graphs with a single source and a single sink. Indeed, our result, together with a recent work of Bekos et al. (Theor Comput Sci 946, 2023) that proves the NP-completeness of 2UBE for planar st-graphs, closes the question about the complexity of the kUBE problem for any k. Motivated by this hardness result, we then focus on the 2UBE Testing for planar st-graphs. On the algorithmic side, we present an O (f (β) · n + n 3) -time algorithm for 2UBE Testing, where β is the branchwidth of the input graph and f is a singly-exponential function on β . Since the treewidth and the branchwidth of a graph are within a constant factor from each other, this result immediately yields an FPT algorithm for st-graphs of bounded treewidth. Furthermore, we describe an O(n)-time algorithm to test whether a plane st-graph whose faces have a special structure admits a 2UBE that additionally preserves the plane embedding of the input st-graph. On the combinatorial side, we present two notable families of plane st-graphs that always admit an embedding-preserving 2 UBE. [ABSTRACT FROM AUTHOR]

In this paper, we explore heterogenous information networks in which each vertex represents one entity and the edges reflect linkage relationships. Heterogenous information networks contain vertices of several entity types, such as papers, authors and terms, and hence can fully reflect multiple linkage relationships among different entities. Such a heterogeneous information network is similar to a mixed media graph (MMG). By representing a bibliographic dataset as an MMG, the performance obtained when searching relevant entities (e.g., papers) can be improved. Furthermore, our academic search enables multiple-entity search, where a variety of entity search results are provided, such as relevant papers, authors and conferences, via a one-time query. Explicitly, given a bibliographic dataset, we propose a Global-MMG, in which a global heterogeneous information network is built. When a user submits a query keyword, we perform a random walk with restart (RWR) to retrieve papers or other types of entity objects. To reduce the query response time, algorithm Net-MMG (standing for NetClus-based MMG) is developed. Algorithm Net-MMG first divides a heterogeneous information network into a collection of sub-networks. Afterward, the Net-MMG performs a RWR on a set of selected relevant sub-networks. We implemented our academic search and conducted extensive experiments using the ACM Digital Library. The experimental results show that by exploring heterogeneous information networks and RWR, both the Global-MMG and Net-MMG achieve better search quality compared with existing academic search services. In addition, the Net-MMG has a shorter query response time while still guaranteeing good quality in search results. [ABSTRACT FROM AUTHOR]

This paper proposes a computational method for the reliability of 2-separable networks. Based on graph theory and probability theory, this method simplifies the calculation process by constructing a network equivalent model and designing corresponding algorithms to achieve the efficient evaluation of reliability. Considering independent random failures of edges with equal probability q, this method can accurately calculate the reliability of 2-separable networks, and its effectiveness and accuracy are verified through examples. In addition, to demonstrate the generality of our method, we have also applied it to other 2-separable networks with fractal structures and proposed linear algorithms for calculating their all-terminal reliability. [ABSTRACT FROM AUTHOR]

Distributed time-varying formation technology for multi-agent systems is recently become a research hotspot in formation control field. However, the formation reconfiguration control technology for agents that randomly appeared to fail during maneuvers is rarely studied. In this paper, the topological relations between intelligence are designed by graph theory to simplify the cooperative interaction between multi-agent systems. Moreover, this paper constructs the time-varying configuration of the target formation based on the rigidity graph theory and leader–follower strategy. Drawing on the establishment of the expert experience database in a collaborative process, we innovatively propose the establishment of a graphic library to help the multi-agent system quickly form an affine transformation as soon as it is disabled. Secondly, the improved Hungarian algorithm is adopted to allocate the target point when the first failure occurs. This algorithm incorporates a gradient weighting factor from the auction algorithm to improve the speed of system reconfiguration with minimum path cost. On this basis, a distributed multi-agent control law based on consistency theory is established, and the system's stability can be guaranteed via Lyapunov functions. Finally, the simulation results demonstrate the feasibility and effectiveness of the proposed formation reconfiguration control algorithm in a collaborative environment. [ABSTRACT FROM AUTHOR]

A given special case of NP-complete scheduling problem can be approximated by solving a special case of similar problem with the same precedence graph. We construct a metric space over a set of special cases of this problem and consider the statistical relationship between distance between a pair of special cases of the under consideration and the average error of the approximated solution. Sethi, Gabow, Coffman's and Fujii's algorithms for this problem are used. It is shown that the absolute and the relative error of the objective function decreases over the density of a graph with a fixed number of jobs. In general case, relative non-zero error value increases with the number of jobs. [ABSTRACT FROM AUTHOR]

Community structure is an important feature of complex networks. Detecting overlapping communities in complex networks is a hot research topic in data mining and graph theory, aiming at the shortcomings of community detection algorithm based on seed expansion, such as the instability of community detection results caused by randomly selecting seeds, the similarity of selected seeds leading to similar communities after different seed expansion, and the increase of calculation caused by deleting nodes in the process of seed expansion. This paper proposes an overlapping community detection algorithm based on high-quality subgraph extension in local core regions of the network (OLCRE). First, a novel seed community selection method is designed. By analyzing the sum of node degrees of the subgraph formed by a node and its neighbor nodes in the local core region of the network and the tightness of the internal and external connections of the subgraph, a seed community selection function is proposed. According to this function, high-quality subgraphs are selected from all the local core regions of the network as seed communities. Then, taking the definition of community as the guideline, a new community expansion strategy is proposed. Considering the influence of the neighbor node on the inner and outer connection tightness of the seed community comprehensively, it is determined whether the neighbor node can join the seed community. Finally, after the completion of all seed community expansion, overlapping nodes and possible missing nodes should be simplified and redetected to further improve the quality of community detection. The proposed algorithm is tested on the artificial and real-world networks and compared with several overlapping community detection algorithms. The experimental results verify the effectiveness and feasibility of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop a method for proving almost sure convergence in the Gromov-Hausdorff-Prokhorov topology for a class of models of growing random graphs that generalises Rémy's algorithm for binary trees. We describe the obtained limits using some iterative gluing construction that generalises the famous line-breaking construction of Aldous' Brownian tree, and we characterize some of them using the self-similarity property in law that they satisfy. To do that, we develop a framework in which a metric space is constructed by gluing smaller metric spaces, called blocks, along the structure of a (possibly infinite) discrete tree. Our growing random graphs seen as metric spaces can be understood in this framework, that is, as evolving blocks glued along a growing discrete tree structure. Their scaling limit convergence can then be obtained by separately proving the almost sure convergence of every block and verifying some relative compactness property for the whole structure. For the particular models that we study, the discrete tree structure behind the construction has the distribution of an affine preferential attachment tree or a weighted recursive tree. We strongly rely on results concerning those two models and their connection, obtained in the companion paper Sénizergues (2021). [ABSTRACT FROM AUTHOR]

Manifold fitting is a manifold verification technique for data with noise and manifold structures. By extracting the expected manifold structure, the reliability of the data manifold hypothesis can be determined, and the true structure of the data without noise can conform to a manifold. This paper proposes a manifold fitting algorithm for the variable-scale spectral graph theory and estimates the deviation of the manifold structure caused by noise. Considering the scale variations in frequency-domain analysis based on spectral graph theory, details of the data under the effect of small scale and characteristics of data shape under the effect of large scale are highlighted. This study uses the average calculation and meanshift method to obtain two types of mean vectors from each neighborhood, which are essential in suppressing noise and maintaining shape, respectively. Therefore, manifold fitting is carried out from two aspects, specifically weakening noise and characterizing the manifold shape. To obtain a closer estimate of the deviation caused by noise to the manifold structure, this study also estimates the neighborhood distribution of data under the effect of medium scale, obtains the covariance information of each neighborhood, and uses the variance information to estimate the manifold structure deviations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the simplest class of stratified spaces linearly embedded graphs. We present an algorithm that learns the abstract structure of an embedded graph and models the specific embedding from a point cloud sampled from it. We use tools and inspiration from computa-tional geometry, algebraic topology, and topological data analysis and prove the correctness of the identified abstract structure under assumptions on the embedding. The algorithm is implemented in the Julia package Skyler, which we used for the numerical simulations in this paper. [ABSTRACT FROM AUTHOR]

Optimal stopping is a fundamental class of stochastic dynamic optimization problems with numerous applications in finance and operations management. In "A nonparametric algorithm for optimal stopping based on robust optimization," the author introduces an approach based on robust optimization for computing near-optimal solutions for computationally demanding stochastic optimal stopping problems with known probability distributions. Through this new use of robust optimization, the paper develops new algorithms for solving stochastic optimal stopping problems that are practical and can outperform state-of-the-art simulation-based algorithms in the context of pricing high-dimensional financial options. Optimal stopping is a fundamental class of stochastic dynamic optimization problems with numerous applications in finance and operations management. We introduce a new approach for solving computationally-demanding stochastic optimal stopping problems with known probability distributions. The approach uses simulation to construct a robust optimization problem that approximates the stochastic optimal stopping problem to any arbitrary accuracy; we then solve the robust optimization problem to obtain near-optimal Markovian stopping rules for the stochastic optimal stopping problem. In this paper, we focus on designing algorithms for solving the robust optimization problems that approximate the stochastic optimal stopping problems. These robust optimization problems are challenging to solve because they require optimizing over the infinite-dimensional space of all Markovian stopping rules. We overcome this challenge by characterizing the structure of optimal Markovian stopping rules for the robust optimization problems. In particular, we show that optimal Markovian stopping rules for the robust optimization problems have a structure that is surprisingly simple and finite-dimensional. We leverage this structure to develop an exact reformulation of the robust optimization problem as a zero-one bilinear program over totally unimodular constraints. We show that the bilinear program can be solved in polynomial time in special cases, establish computational complexity results for general cases, and develop polynomial-time heuristics by relating the bilinear program to the maximal closure problem from graph theory. Numerical experiments demonstrate that our algorithms for solving the robust optimization problems are practical and can outperform state-of-the-art simulation-based algorithms in the context of widely-studied stochastic optimal stopping problems from high-dimensional option pricing. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2023.2461. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we approach a method of clustering binary signature of image in order to create a clustering graph structure for building the content‐based image retrieval. First, the paper presents the segmentation method based on low‐level visual features including colour and texture of image. On the basis of segmented image, the paper creates binary signature to describe location, colour, and shape of interest objects. In order to match similar images, the paper presents a similarity measure between the images based on binary signature. From that, the paper proposes the method of clustering binary signature to quickly query similar images. At the same time, the graph data structure is built using the partition cluster technique and the rules of binary signatures' distribution of images. On the basis of data structure, we propose a graph creation algorithm, a cluster splitting/merging algorithm, and a similarity image retrieval algorithm. To illustrate the proposed theory, we build an image retrieval application and assess the experimental results on the image datasets including COREL (1,000 images), CBIR images (1,344 images), WANG (10,800 images), MSRDI (15,720 images), and ImageCLEF (20,000 images). [ABSTRACT FROM AUTHOR]

In practical applications of graph theory, indeterminacy factors always appear in graphs. Uncertain random graph was proposed via chance theory, in which some edges exist with degrees in probability measure and others exist with degrees in uncertain measure. This paper discusses the contributions of edges for connectivity of an uncertain random graph and proposes concepts about significance of edges, according to which edges are classified. In addition, this paper presents algorithms for calculating connectivity index and significance of edges of an uncertain random graph. Examples are given to illustrate algorithms and methods. [ABSTRACT FROM AUTHOR]

As a generalization of graphs and simplicial complexes, hypergraphs have various applications in chemistry, biology, computer science and data science. Recently, the first well-defined hypergraph-based embedded homology and persistent (embedded) homology models have been proposed and achieved great success in drug design. However, the further applications of these models have been significantly hindered by the lack of efficient computational algorithms. In this paper, we propose an algorithm for embedded homology and persistent (embedded) homology of hypergraphs over field coefficient. One of the key issues for hypergraph-based homology models is the absence of proper boundary operators as in traditional simplicial complex-based models. A supremum/infimum chain complex has been proposed in the embedded homology model with well-defined boundary operators. Here we give detailed algorithms for transforming a filtered hypergraph to its filtered infimum chain complex and supremum chain complex. In this way, the general algorithm for chain complex can be used directly on the supremum/infimum chain complexes. Our algorithm has been validated on hypergraph models of protein structures from the protein data bank. It has been found that our algorithm is very robust and efficient. [ABSTRACT FROM AUTHOR]

This paper introduces the use of graph theory for the study of the work of Candilis–Josic–Woods. Α short introduction to the architects' main strategies as members of Team Χ and CIAM (Congrès Internationaux d'Architecture Moderne) critics is given. Geometry and computational design methods for city planning and design are briefly discussed. Definitions of the minimum spanning tree, the shortest walk tree and the Steiner tree are then developed. The research projects these methods onto the main principles of Candilis–Josic–Woods' planning and urban design approach to reinforce their strategic concepts. Distance-related and proximity-based ideas and their importance are sought in the literature related to Candilis–Josic–Woods' body of work. Algorithmic based examples approximating a Euclidean Steiner tree are shown and discussed in the context of Candilis–Josic–Woods' syntax. This paper argues that the generation of additional points through the use of a Euclidean Steiner tree algorithmic process is of importance in the work of Candilis–Josic–Woods as it allows for a systematic but emerging creation of hubs that can be activated as space on the one hand, and facilitate pedestrian circulation on the other. The project seeks to demonstrate the relevance of the triplet's design methods to today's complex networks of urban environments. [ABSTRACT FROM AUTHOR]

Resource-efficient technologies for cutting sheet materials allow for the contours of cut-off details to be overlapped. This includes the Intermittent Cutting Problem and the Endpoint Cutting Problem. This paper reviews mathematical models of such resource-efficient cutting processes and suggests algorithms for defining the cutter route under technological constraints. As soon as a cutting plan is given, optimisation with shortening the total length of idle passes. No information of the detail shape is required to define the sequence of detail cutting. This is why all curves without self-intersections and contiguities that are a constituent part of detail boundaries may be interpreted as edges of the plane graph G, and all points of intersection and contiguity may be interpreted as vertices of the graph G. Up to homeomorphism, plane graph G can be represented by a list of edges with incident vertices and faces . This allows the restrictions of the planed cutter trajectory to be formalised in terms of graph theory. A series of algorithms for constructing the permitted route in the plane graph G as an image of the cutting plan is suggested. The constructed route for the graph G can be interpreted as a tool trajectory for the cutting plan which is the inverse image of graph G. [ABSTRACT FROM AUTHOR]

Detection of communities is one of the prominent characteristics of vast and complex networks like social networks, collaborative networks, and web graphs. In the modern era, new users get added to these complex networks, which results in an expansion of application-generated networks. Extracting relevant information from these large networks has become one of the most prominent research areas. Community detection tries to reduce the application-generated graph into smaller communities in which nodes within the community are similar. Most of the recent proposals are focused on detecting overlapping communities in the network with higher accuracy. An integral issue in graph theory is the enumeration of cliques in a larger graph. As clique is a group of completely connected nodes which shows the explicit communities means these nodes share the same types of information. Clique-based community detection algorithm utilizing the clique property of the graph also identifies the implicit communities, which is not directly shown in the graph. Many overlapping community detection algorithms are proposed by researchers that rely on cliques. The goal of this paper is to offer a comparative analysis of clique-based community detection algorithms. This paper provides a pervasive survey on research works identifying the cliques in a network for detecting overlapping communities. We bring together most of the state-of-the-art clique-based community detection algorithms into a single article with their accessible benchmark data sets. It presents a detailed description of methods based on K-cliques, maximal cliques, and triad percolation methods and addresses these approaches' challenges. Finally, the comparative analysis of overlapping community detection methodologies is also reported. [ABSTRACT FROM AUTHOR]

In the current era of increasingly complex social life, as people's demand quality is getting higher and higher, the solution of the problem often has multiple indicators to achieve the optimum. This forces the graph coloring problem (GCP) to become complicated, and it is difficult to directly obtain the optimal solution, which brings new challenges to the solution of the problem. In response to this problem, the GCP field is of great research significance. With the in-depth study of GCP, the research on multiobjective optimization (MOO) in graph coloring algorithm (GCA) is gradually carried out. Its performance advantage is of great significance for solving multicondition constraint problems. This paper aims to study the application of Genetic Algorithm (GA) in GCA. Through the analysis and research of GA, and the fusion of numerical analysis and scientific computing, it can be applied to the construction of the neighbor distinguishable uniform V-full coloring algorithm (AVDEVTCA) to solve the AVDEVTC problem. This paper describes the basic theory of MOO and graph coloring. It conducts an experimental analysis of the algorithm performance and uses the relevant theoretical formulas to explain it. The results show that the algorithm takes 5754.142 S seconds to test 21325415 images and can color a large number of results that cannot be done manually in less time. It has greatly improved in terms of time and manpower saving and greatly improved practicability and work efficiency. [ABSTRACT FROM AUTHOR]

This paper deals with a generalization of polyominoes called (a, b)-connected discrete figures, where a and b respectively denotes the connectivity of the foreground (i.e. black pixels) and background (i.e. white pixels). Formally, a finite set of pixels P is (a, b)-connected if P is a-connected and P̄ is b-connected. By adapting a combinatorial structure enumeration algorithm due to Martin, we successfully generate (a, b)-connected discrete figures up to size n = 18. [ABSTRACT FROM AUTHOR]

A greedy randomized adaptive search procedure (GRASP) is a metaheuristic for combinatorial optimization. It is a multi-start or iterative process, in which each GRASP iteration consists of two phases, a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Since 1989, numerous papers on the basic aspects of GRASP, as well as enhancements to the basic metaheuristic, have appeared in the literature. GRASP has been applied to a wide range of combinatorial optimization problems, ranging from scheduling and routing to drawing and turbine balancing. This is the second of two papers with an annotated bibliography of the GRASP literature from 1989 to 2008. In the companion paper, algorithmic aspects of GRASP are surveyed. In this paper, we cover the literature where GRASP is applied to scheduling, routing, logic, partitioning, location, graph theory, assignment, manufacturing, transportation, telecommunications, biology and related fields, automatic drawing, power systems, and VLSI design. [ABSTRACT FROM AUTHOR]

We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property of being isomorphic to a directed graph. In particular, we show that, as a consequence of the properties associated with the MAG structure, a MAG can be represented in matrix form. Moreover, we also show that any possible MAG function (algorithm) can be obtained from this matrix-based representation. This is an important theoretical result since it paves the way for adapting well-known graph algorithms for application in MAGs. We present a set of basic MAG algorithms, constructed from well-known graph algorithms, such as degree computing, Breadth First Search (BFS), and Depth First Search (DFS). These algorithms adapted to the MAG context can be used as primitives for building other more sophisticated MAG algorithms. Therefore, such examples can be seen as guidelines on how to properly derive MAG algorithms from basic algorithms on directed graphs. We also make available Python implementations of all the algorithms presented in this paper. [ABSTRACT FROM AUTHOR]

For large-scale engineering problems, it has been generally accepted that domain-partitioning algorithms are highly desirable for general-purpose finite element analysis (FEA). This paper presents a heuristic numerical algorithm that can efficiently partition any transportation network (or any finite element mesh) into a specified number of subdomains (usually depending on the number of parallel processors available on a computer), which will result in "minimising the total number of system BOUNDARY nodes" (as a primary criterion) and achieve "balancing work loads" amongst the subdomains (as a secondary criterion). The proposed seven-step heuristic algorithm (with enhancement features) is based on engineering common sense and observation. This current work has the following novelty features: (i) complicated graph theories that are NOT needed and (ii) unified treatments of transportation networks (using line elements) and finite element (FE) meshes (using triangular, tetrahedral, and brick elements) that can be performed through transforming the original network (or FE mesh) into a pseudo-transportation network which only uses line elements. Several examples, including real-life transportation networks and finite element meshes (using triangular/brick/tetrahedral elements) are used (under MATLAB computer environments) to explain, validate and compare the proposed algorithm's performance with the popular METIS software. [ABSTRACT FROM AUTHOR]

Fault diagnosis of interconnection networks is vital to ensuring the reliability and maintenance of multiprocessor systems. Based on graph theory, diagnostic algorithms for solving the problem of fault diagnosis in interconnection networks have been widely studied. As the number of processors in multiprocessor systems has increased in recent years, fault diagnosis algorithms based on graph theory cannot meet the current diagnosis requirements of some interconnection networks, such as t-diagnosable systems. In this paper, we use the evolution diagnosis approach to study fault diagnosis in t-diagnosable systems under the PMC model. First, for a t-diagnosable system G with a syndrome σ , we use a simple centralized algorithm to generate its simplified diagnosis graph G f , which contains all the faulty nodes in G. Based on the graph, we prove that the faulty node set in G is the minimum cover set of G f . Next, we prove that the problem of computing the minimum cover set for G f is equivalent to the problem of computing the optimal solution of a zero-one integer program. Using this result, we propose a novel genetic algorithm to solve the problem of the zero-one integer program. The simulation results show that the diagnostic accuracy of our proposed algorithm is equal to or greater than 96% and that the proposed algorithm outperforms its competitors in terms of diagnostic accuracy, number of iterations and running time. [ABSTRACT FROM AUTHOR]

Indoor space information is the basis of indoor location services such as indoor navigation, path planning, emergency evacuation, etc. Focusing on indoor navigation needs, this paper proposes a fast construction algorithm for a complex indoor space topology model based on disjoint set for the problem of lacking polygon description and topological relationship expression of indoor space entity objects in building plan drawings. Firstly, the Tarjan algorithm is used for identifying the hanging edges existing in the indoor space. Secondly, each edge is stored as two different edges belonging to two adjacent polygons that share the edge. A ring structure is introduced to judge the geometric position of walls, and then an efficient disjoint set algorithm is used to perform set merging. After that, disjoint set is queried to obtain all indoor space contours and external boundary contours, thereby the complete indoor space topological relationship at multiple levels is established. Finally, the connectivity theory of graph is used for solving the problem of a complex isolated polygon in topology information generation. The experimental results show that the proposed algorithm has generality to efficiently complete the automatic construction of a topological model for complex scenarios, and effectively acquire and organize indoor space information, thus providing a good spatial cognition mode for indoor navigation. [ABSTRACT FROM AUTHOR]

The Hamiltonian cycle problem is one of the most important problems in graph theory that has many applications. This problem is NP-complete for general grid graphs. For solid grid graphs, there are polynomial-time algorithms. Existence of polynomial-time algorithms for grid graphs with few holes has been asked in the literature. In this paper, we give a linear-time algorithm for rectangular grid graphs with two rectangular holes. This extends the previous result for rectangular grid graphs with one rectangular hole. We first present the forbidden conditions in which there is no Hamiltonian cycle for any grid graphs, including rectangular grid graphs with rectangular holes. We then show that if these forbidden conditions do not hold, then there exists a Hamiltonian cycle. The proof is constructive, therefore, it gives an algorithm. An application of the problem is in off-line robot exploration. [ABSTRACT FROM AUTHOR]

In graph theory, domination number and its variants such as total domination number are studied by many authors. Let the domination number and the total domination number of a graph G without isolated vertices be γ(G) and γt(G), respectively. Based on the inequality γt(G) ≤ 2γ(G), we investigate the graphs satisfying the upper bound, that is, graphs G with γt(G) = 2γ(G). In this paper, we present some new properties of such graphs and provide an algorithm which can determine whether γt(G) = 2γ(G) or not for a family of graphs not covered by the previous results in the literature. [ABSTRACT FROM AUTHOR]

The shortest path problem (SPP) in graph theory is the problem of assessing a path between two vertices in a graph to minimize the sum of the weights of the edges of its constituent. The SPP ia classical and elementry problem of a graph theory which is applicable in many fields like GIS network analysis, computational geometry, operational research and graph algorithms. SPP are among the elementry problems studied in network optimization. Graphs are very important models of networks. Path-solutions, including location-based services and webbased GIS services, are becoming an important component of many GIS applications. In this paper, we introduced a new method to solve SPP in a network. The SPP is fundamental problems in network optimization. Most traditional solutions for path-finding depends on the shortest path algorithms which tend to minimize travel cost between points. These algorithms use cost criteria which are generally the edge attribute of the graph network. There is a neutrosophical shortest path study in this paper with a vague neutrosophic number (VNsN) on a network. A suggested algorithm also provides the shortest path length (SPL) from source vertex to destination vertex with the ranking function. Here, a VNsN is allocated to each arc length. Lastly, there is a numerical example showing the method proposed. [ABSTRACT FROM AUTHOR]

Phylogenetic networks generalize phylogenetic trees by allowing the modelization of events of reticulate evolution. Among the different kinds of phylogenetic networks that have been proposed in the literature, the subclass of binary tree-child networks is one of the most studied ones. However, very little is known about the combinatorial structure of these networks. In this paper we address the problem of generating all possible binary tree-child (BTC) networks with a given number of leaves in an efficient way via reduction/augmentation operations that extend and generalize analogous operations for phylogenetic trees, and are biologically relevant. Since our solution is recursive, this also provides us with a recurrence relation giving an upper bound on the number of such networks. We also show how the operations introduced in this paper can be employed to extend the evolutive history of a set of sequences, represented by a BTC network, to include a new sequence. An implementation in python of the algorithms described in this paper, along with some computational experiments, can be downloaded from . [ABSTRACT FROM AUTHOR]

Energy recharging has received much attention now because of the development of wireless recharging technology. This paper proposes a greedy constructing tree algorithm for shortest path in perpetual wireless recharging wireless sensor networks (GCTA) which enables the recharger to work while moving through the shortest path. The algorithm can construct the shorter path which passes all the sensors only once and guarantees that each sensor will be fully recharged. It computes the path in advance with lower complexity. And it also uses the graph theory, the tree theory, the Markov chain theorem and the powerful computing function of a computer. The contributions of the paper are itemized as follows: guaranteeing all the sensors to be fully recharged only once and reducing the length of the recharging path through constructing the greedy tree. In the experiment, this algorithm can construct the shorter path. So it is novel, general and can be applied widely. [ABSTRACT FROM AUTHOR]

As a tool of qualitative representation, conditional preference network (CP-net) has recently become a hot research topic in the field of artificial intelligence. The semantics of CP-nets does not restrict the generation of cycles, but the existence of the cycles would affect the property of CP-nets such as satisfaction and consistency. This paper attempts to use the feedback set problem theory including feedback vertex set (FVS) and feedback arc set (FAS) to cut cycles in CP-nets. Because of great time complexity of the problem in general, this paper defines a class of the parent vertices in a ring CP-nets firstly and then gives corresponding algorithm, respectively, based on FVS and FAS. Finally, the experiment shows that the running time and the expressive ability of the two methods are compared. [ABSTRACT FROM AUTHOR]

Broadcasting is disseminating information in a network where a specific message must spread to all network vertices as quickly as possible. Finding the minimum broadcast time of a vertex in an arbitrary network is proven to be NP-complete. However, this problem is solvable for a few families of networks. In this paper, we present an optimal algorithm for finding the broadcast time of any vertex in a fully connected tree ( FCT n ) in O (| V | log log n) time. An FCT n is formed by attaching arbitrary trees to vertices of a complete graph of size n where | V | is the total number of vertices in the graph. [ABSTRACT FROM AUTHOR]

Damage detection through an inverse optimization problem has been investigated by many researchers. Recently, Modal Strain Energy (MSE) has been utilized as an index (MSEBI) for damage localization that serves to guide the optimization. This guided approach considerably reduces the computational cost and increases the accuracy of optimization. Although this index mostly exhibits an acceptable performance, it fails to find some damaged elements' locations in some cases. The aim of this paper is twofold. Firstly, a Graph-based Adaptive Threshold (GAT) is proposed to identify some of those elements that are not detected by basic MSEBI. GAT relies on the concepts from graph theory and MSE working as a simple anomaly detection technique. Secondly, an Improved version of the Water Strider Algorithm (IWSA) is introduced, applied to the damage detection problems with incomplete modal data and noisecontaminated inputs. Several optimization algorithms, including the newly-established Water Strider Algorithm (WSA), are utilized to test the proposed method. The investigations on several damage detection problems demonstrate the GAT and IWSA's satisfactory performance compared to the previous methods. [ABSTRACT FROM AUTHOR]

The history of infections and epidemics holds famous examples where understanding, containing, and ultimately treating an outbreak began with understanding its mode of spread. Influenza, HIV, and most computer viruses spread person to person, device to device, and through contact networks; Cholera, Cancer, and seasonal allergies, on the other hand, do not. In this paper, we study two fundamental questions of detection. First, given a snapshot view of a (perhaps vanishingly small) fraction of those infected, under what conditions is an epidemic spreading via contact (e.g., Influenza), distinguishable from a random illness operating independently of any contact network (e.g., seasonal allergies)? Second, if we do have an epidemic, under what conditions is it possible to determine which network of interactions is the main cause of the spread—the causative network—without any knowledge of the epidemic, other than the identity of a minuscule subsample of infected nodes? The core, therefore, of this paper, is to obtain an understanding of the diagnostic power of network information. We derive sufficient conditions that networks must satisfy for these problems to be identifiable, and produce efficient, highly scalable algorithms that solve these problems. We show that the identifiability condition we give is fairly mild, and in particular, is satisfied by two common graph topologies: the $d$ -dimensional grid, and the Erdös-Renyi graphs. [ABSTRACT FROM AUTHOR]

There are some interesting properties in quantum mechanics, such as quantum superposition and entanglement. We can use these features to solve some specific problems. Quantum computer has more advantages than classical computer in many problems. In this paper, we are interested in regular graph. A special case of graph structure destroyed is given. We present a search algorithm to find exceptional vertexes in the graph in this case. The algorithm uses the trick of amplitude amplification in quantum search algorithm. In the corresponding classical algorithm, the adjacency matrix may be used to store the information of vertex and edge of graph. It takes one time for the best and N times for the worst to find the target. Which means that N/2 times on average need to be conducted. In our quantum algorithm, nodes and vertexes are stored in quantum states, using quantum search to design algorithm. The search process can be accelerated in our quantum algorithm. [ABSTRACT FROM AUTHOR]

This paper deals with an analysis of three algorithms for the graph vertex cover problem. Certain methods for solving this problem are analyzed. In addition, different studies on the problem and some approaches to its solution are discussed as well. An exact algorithm (based on the backtracking approach) is presented. Calculating the average time for execution of this algorithm is consistent with the multitasking way of work of the operating system. For this purpose, four different starts of the algorithm are made and then the average time of all of them is calculated. The exact algorithm found the optimal solutions for all analyzed graphs. Besides this algorithm, two other heuristic algorithms for solving the problem are discussed. For this study, an interactive application is developed to visualize the performance of the three algorithms and display the obtained results. The results show that for small graphs with no more than 25 vertices, the exact algorithm can be used to solve optimally the graph vertex cover problem. For the largest graphs, none of the two heuristic algorithms found the optimal solutions, but these algorithms generated solutions that are very close to the optimal ones. In summary, when the size of the graph increases linearly, the execution time of the heuristic algorithms increases linearly, while the execution time of the exact algorithm increases exponentially. [ABSTRACT FROM AUTHOR]