Related papers: A Note on Max $k$-Vertex Cover: Faster FPT-AS, Sma…

We propose a \textit{purely combinatorial algorithm} for \mkvc{} in bipartite graphs, achieving approximation ratio~0.7. The only combinatorial algorithms currently known until now for this problem are the natural greedy algorithm, that…

Let $G=(V,E)$ be a simple undirected graph. The open neighbourhood of a vertex $v$ in $G$ is defined as $N_G(v)=\{u\in V~|~ uv\in E\}$; whereas the closed neighbourhood is defined as $N_G[v]= N_G(v)\cup \{v\}$. For an integer $k$, a subset…

We study the classic Max-Cut problem under multiple cardinality constraints, which we refer to as the Constrained Max-Cut problem. Given a graph $G=(V, E)$, a partition of the vertices into $c$ disjoint parts $V_1, \ldots, V_c$, and…

We study the Densest At-Least-$k$-Subgraph (DAL$k$S) problem, in which we are given an undirected graph $G$ and an integer $k$, and the goal is to find a subgraph of $G$ with at least $k$ vertices with maximum density. The best-known…

We study the problem of computing the minimum vertex cover on k-uniform k-partite hypergraphs when the k-partition is given. On bipartite graphs (k = 2), the minimum vertex cover can be computed in polynomial time. For general k, the…

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…

A graph $H$ is {\em $p$-edge colorable} if there is a coloring $\psi: E(H) \rightarrow \{1,2,\dots,p\}$, such that for distinct $uv, vw \in E(H)$, we have $\psi(uv) \neq \psi(vw)$. The {\sc Maximum Edge-Colorable Subgraph} problem takes as…

Given a $k$-vertex-connected graph $G$ and a set $S$ of extra edges (links), the goal of the $k$-vertex-connectivity augmentation problem is to find a set $S' \subseteq S$ of minimum size such that adding $S'$ to $G$ makes it…

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…

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).…

We present a packing-based approximation algorithm for the $k$-Set Cover problem. We introduce a new local search-based $k$-set packing heuristic, and call it Restricted $k$-Set Packing. We analyze its tight approximation ratio via a…

We study two related problems: finding a set of k vertices and minimum number of edges (kmin) and finding a graph with at least m' edges and minimum number of vertices (mvms). Goldschmidt and Hochbaum \cite{GH97} show that the mvms problem…

Let F be a finite set of graphs. In the F-Deletion problem, we are given an n-vertex graph G and an integer k as input, and asked whether at most k vertices can be deleted from G such that the resulting graph does not contain a graph from F…

A prototypical graph problem is centered around a graph-theoretic property for a set of vertices and a solution to it is a set of vertices for which the desired property holds. The task is to decide whether, in the given graph, there exists…

We present improved approximation algorithms for some problems in the related areas of Capacitated Network Design and Flexible Graph Connectivity. In the Cap-$k$-ECSS problem, we are given a graph $G=(V,E)$ whose edges have non-negative…

The k-Clique problem is a canonical hard problem in parameterized complexity. In this paper, we study the parameterized complexity of approximating the k-Clique problem where an integer k and a graph G on n vertices are given as input, and…

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…

We study approximation algorithms for the following geometric version of the maximum coverage problem: Let $\mathcal{P}$ be a set of $n$ weighted points in the plane. Let $D$ represent a planar object, such as a rectangle, or a disk. We…

In the Subset Feedback Arc Set in Tournaments, Subset-FAST problem we are given as input a tournament $T$ with a vertex set $V(T)$ and an arc set $A(T)$, along with a terminal set $S \subseteq V(T)$, and an integer $ k$. The objective is to…

Given a graph, a $k$-plex is a set of vertices in which each vertex is not adjacent to at most $k-1$ other vertices in the set. The maximum $k$-plex problem, which asks for the largest $k$-plex from the given graph, is an important but…