Related papers: Deterministic parameterized connected vertex cover
We consider a generalized version of the (weighted) one-center problem on graphs. Given an undirected graph $G$ of $n$ vertices and $m$ edges and a positive integer $k\leq n$, the problem aims to find a point in $G$ so that the maximum…
We investigate the complexity of several fundamental polynomial-time solvable problems on graphs and on matrices, when the given instance has low treewidth; in the case of matrices, we consider the treewidth of the graph formed by non-zero…
In the $l$-path vertex cover problem the input is an undirected graph $G$ and an integer $k$. The goal is to decide whether there is a set of vertices $S$ of size at most $k$ such that $G-S$ does not contain a path with $l$ vertices. In…
We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank $f$. This problem is equivalent to the Minimum Weight Set Cover problem in which the frequency of every…
A $k$-matching cover of a graph $G$ is a union of $k$ matchings of $G$ which covers $V(G)$. A matching cover of $G$ is optimal if it consists of the fewest matchings of $G$. In this paper, we present an algorithm for finding an optimal…
We study the problem of estimating the size of maximum matching and minimum vertex cover in sublinear time. Denoting the number of vertices by $n$ and the average degree in the graph by $\bar{d}$, we obtain the following results for both…
We give an algorithm that for an input n-vertex graph G and integer k>0, in time 2^[O(k)]n either outputs that the treewidth of G is larger than k, or gives a tree decomposition of G of width at most 5k+4. This is the first algorithm…
Given an $n$-vertex bipartite graph $I=(S,U,E)$, the goal of set cover problem is to find a minimum sized subset of $S$ such that every vertex in $U$ is adjacent to some vertex of this subset. It is NP-hard to approximate set cover to…
We give a deterministic polynomial space construction for nearly optimal eps-nets with respect to any input n-dimensional convex body K and norm |.|. More precisely, our algorithm can build and iterate over an eps-net of K with respect to…
In this paper, we develop a distributed algorithm for solving a class of distributed convex optimization problems where the local objective functions can be a general nonsmooth function, and all equalities and inequalities are network-wide…
Partitioning a connected graph into $k$~vertex-disjoint connected subgraphs of similar (or given) orders is a classical problem that has been intensively investigated since late seventies. Given a connected graph $G=(V,E)$ and a weight…
Given an edge-weighted graph $G$ on $n$ nodes, the NP-hard Max-Cut problem asks for a node bipartition such that the sum of edge weights joining the different partitions is maximized. We propose a fixed-parameter tractable algorithm…
In the vertex connectivity problem, given an undirected $n$-vertex $m$-edge graph $G$, we need to compute the minimum number of vertices that can disconnect $G$ after removing them. This problem is one of the most well-studied graph…
A book embedding of a graph is a drawing that maps vertices onto a line and edges to simple pairwise non-crossing curves drawn into pages, which are half-planes bounded by that line. Two-page book embeddings, i.e., book embeddings into 2…
We consider the problem of maintaining an (approximately) minimum vertex cover in an $n$-node graph $G = (V, E)$ that is getting updated dynamically via a sequence of edge insertions/deletions. We show how to maintain a…
We consider graphs without loops or parallel edges in which every edge is assigned + or -. Such a signed graph is balanced if its vertex set can be partitioned into parts $V_1$ and $V_2$ such that all edges between vertices in the same part…
Cutwidth of a digraph is a width measure introduced by Chudnovsky, Fradkin, and Seymour [4] in connection with development of a structural theory for tournaments, or more generally, for semi-complete digraphs. In this paper we provide an…
The Maximum Induced Matching problem asks to find the maximum $k$ such that, given a graph $G=(V,E)$, can we find a subset of vertices $S$ of size $k$ for which every vertices $v$ in the induced graph $G[S]$ has exactly degree $1$. In this…
In the online disjoint set covers problem, the edges of a hypergraph are revealed online, and the goal is to partition them into a maximum number of disjoint set covers. That is, n nodes of a hypergraph are given at the beginning, and then…
In this work, we study the trade-off between the running time of approximation algorithms and their approximation guarantees. By leveraging a structure of the `hard' instances of the Arora-Rao-Vazirani lemma [JACM'09], we show that the…