Related papers: An improved algorithm for the vertex cover $P_3$ p…
Generally, a graph G, an independent set is a subset S of vertices in G such that no two vertices in S are adjacent (connected by an edge) and a vertex cover is a subset S of vertices such that each edge of G has at least one of its…
This work introduces two techniques for the design and analysis of branching algorithms, illustrated through the case study of the Vertex Cover problem. First, we present a method for automatically generating branching rules through a…
Given a graph $G$, let $vc(G)$ and $vc^+(G)$ be the sizes of a minimum and a maximum minimal vertex covers of $G$, respectively. We say that $G$ is well covered if $vc(G)=vc^+(G)$ (that is, all minimal vertex covers have the same size).…
The VertexCover problem is proven to be computationally hard in different ways: It is NP-complete to find an optimal solution and even NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on…
We consider a natural generalization of Vertex Cover: the Subset Vertex Cover problem, which is to decide for a graph $G=(V,E)$, a subset $T\subseteq V$ and integer $k$, if $V$ has a subset $S$ of size at most $k$, such that $S$ contains at…
The goal in the stochastic vertex cover problem is to obtain an approximately minimum vertex cover for a graph $G^\star$ that is realized by sampling each edge independently with some probability $p\in (0, 1]$ in a base graph $G = (V, E)$.…
Given a graph $G=(V,E)$, a vertex $u \in V$ {\em ve-dominates} all edges incident to any vertex of $N_G[u]$. A set $S \subseteq V$ is a {\em ve-dominating set} if for all edges $e\in E$, there exists a vertex $u\in S$ such that $u$…
It is well-known that the Vertex Cover problem is in P on bipartite graphs, however; the computational complexity of the Partial Vertex Cover problem on bipartite graphs is open. In this paper, we first show that the Partial Vertex Cover…
We consider a natural generalization of the Partial Vertex Cover problem. Here an instance consists of a graph G = (V,E), a positive cost function c: V-> Z^{+}, a partition $P_1,..., P_r$ of the edge set $E$, and a parameter $k_i$ for each…
We present a dynamic programming algorithm for optimally solving the Cograph Editing problem on an $n$-vertex graph that runs in $O(3^n n)$ time and uses $O(2^n)$ space. In this problem, we are given a graph $G = (V, E)$ and the task is to…
The paper presents an algorithm for minimum vertex cover problem, which is an NP-Complete problem. The algorithm computes a minimum vertex cover of each input simple graph. Tested by the attached MATLAB programs, Stage 1 of the algorithm is…
Given a graph $G=(V,E)$ with two distinguished vertices $s,t\in V$ and an integer parameter $L>0$, an {\em $L$-bounded cut} is a subset $F$ of edges (vertices) such that the every path between $s$ and $t$ in $G\setminus F$ has length more…
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. These graphs and their generalizations were applied in various fields, including modeling channel routing…
We give a parameterized algorithm for weighted vertex cover on graphs with maximum degree 3 whose time complexity is $O^*(1.402^t)$, where $t$ is the minimum size of a vertex cover of the input graph.
The widely studied edge modification problems ask how to minimally alter a graph to satisfy certain structural properties. In this paper, we introduce and study a new edge modification problem centered around transforming a given graph into…
There are many classical problems in P whose time complexities have not been improved over the past decades. Recent studies of "Hardness in P" have revealed that, for several of such problems, the current fastest algorithm is the best…
This study considers the (soft) capacitated vertex cover problem in a dynamic setting. This problem generalizes the dynamic model of the vertex cover problem, which has been intensively studied in recent years. Given a dynamically changing…
In the Telephone Broadcast problem we are given a graph $G=(V,E)$ with a designated source vertex $s\in V$. Our goal is to transmit a message, which is initially known only to $s$, to all vertices of the graph by using a process where in…
The eternal vertex cover problem is a dynamic variant of the classical vertex cover problem. It is NP-hard to compute the eternal vertex cover number of graphs and known algorithmic results for the problem are very few. This paper presents…
The CONTRACTION(vc) problem takes as input a graph $G$ on $n$ vertices and two integers $k$ and $d$, and asks whether one can contract at most $k$ edges to reduce the size of a minimum vertex cover of $G$ by at least $d$. Recently, Lima et…