Related papers: A Faster Randomized Algorithm for Vertex Cover: An…
We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…
The vertex-cover problem is studied for random graphs $G_{N,cN}$ having $N$ vertices and $cN$ edges. Exact numerical results are obtained by a branch-and-bound algorithm. It is found that a transition in the coverability at a $c$-dependent…
Counting the frequency of small subgraphs is a fundamental technique in network analysis across various domains, most notably in bioinformatics and social networks. The special case of triangle counting has received much attention. Getting…
Mining cohesive subgraphs from a graph is a fundamental problem in graph data analysis. One notable cohesive structure is $\gamma$-quasi-clique (QC), where each vertex connects at least a fraction $\gamma$ of the other vertices inside.…
Coverage problems are central in optimization and have a wide range of applications in data mining and machine learning. While several distributed algorithms have been developed for coverage problems, the existing methods suffer from…
A common approach for designing scalable algorithms for massive data sets is to distribute the computation across, say $k$, machines and process the data using limited communication between them. A particularly appealing framework here is…
Minimum vertex cover problem is an NP-Hard problem with the aim of finding minimum number of vertices to cover graph. In this paper, a learning automaton based algorithm is proposed to find minimum vertex cover in graph. In the proposed…
We present a local algorithm (constant-time distributed algorithm) for finding a 3-approximate vertex cover in bounded-degree graphs. The algorithm is deterministic, and no auxiliary information besides port numbering is required.
Finding a minimum vertex cover in a network is a fundamental NP-complete graph problem. One way to deal with its computational hardness, is to trade the qualitative performance of an algorithm (allowing non-optimal outputs) for an improved…
Given a graph $G=(V,E)$ and a positive integer $t\geq2$, the task in the vertex cover $P_t$ ($VCP_t$) problem is to find a minimum subset of vertices $F\subseteq V$ such that every path of order $t$ in $G$ contains at least one vertex from…
In this paper we provide an algorithm that generates a graph with given degree sequence uniformly at random. Provided that $\Delta^4=O(m)$, where $\Delta$ is the maximal degree and $m$ is the number of edges,the algorithm runs in expected…
Given an undirected, unweighted graph with $n$ vertices and $m$ edges, the maximum cut problem is to find a partition of the $n$ vertices into disjoint subsets $V_1$ and $V_2$ such that the number of edges between them is as large as…
As massive graphs become more prevalent, there is a rapidly growing need for scalable algorithms that solve classical graph problems, such as maximum matching and minimum vertex cover, on large datasets. For massive inputs, several…
We discuss the problem of embedding graphs in the plane with restrictions on the vertex mapping. In particular, we introduce a technique for drawing planar graphs with a fixed vertex mapping that bounds the number of times edges bend. An…
Many NP-hard problems, such as Dominating Set, are FPT parameterized by clique-width. For graphs of clique-width $k$ given with a $k$-expression, Dominating Set can be solved in $4^k n^{O(1)}$ time. However, no FPT algorithm is known for…
Consider a graph with a rotation system, namely, for every vertex, a circular ordering of the incident edges. Given such a graph, an angle cover maps every vertex to a pair of consecutive edges in the ordering -- an angle -- such that each…
Counting the solution number of combinational optimization problems is an important topic in the study of computational complexity, especially on the #P-complete complexity class. In this paper, we first investigate some organizations of…
Fully dynamic graph is a data structure that (1) supports edge insertions and deletions and (2) answers problem specific queries. The time complexity of (1) and (2) are referred to as the update time and the query time respectively. There…
Finding all maximal $k$-plexes on networks is a fundamental research problem in graph analysis due to many important applications, such as community detection, biological graph analysis, and so on. A $k$-plex is a subgraph in which every…
In the Connected Vertex Cover problem we are given an undirected graph G together with an integer k and we are to find a subset of vertices X of size at most k, such that X contains at least one end-point of each edge and moreover X induces…