English
Related papers

Related papers: Approximating Subdense Instances of Covering Probl…

200 papers

We study the efficient approximability of basic graph and logic problems in the literature when instances are specified hierarchically as in \cite{Le89} or are specified by 1-dimensional finite narrow periodic specifications as in…

Computational Complexity · Computer Science 2007-05-23 Madhav V. Marathe , Harry B. Hunt , Richard E. Stearns , Venkatesh Radhakrishnan

The approximate degree of a Boolean function $f(x_{1},x_{2},\ldots,x_{n})$ is the minimum degree of a real polynomial that approximates $f$ pointwise within $1/3$. Upper bounds on approximate degree have a variety of applications in…

Computational Complexity · Computer Science 2018-01-16 Alexander A. Sherstov

We study approximability of regular constraint satisfaction problems, i.e., CSPs where each variable in an instance has the same number of occurrences. In particular, we show that for any CSP $\Lambda$, existence of an $\alpha$…

Computational Complexity · Computer Science 2020-04-20 Aleksa Stankovic

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…

Computational Geometry · Computer Science 2017-12-08 Kai Jin , Jian Li , Haitao Wang , Bowei Zhang , Ningye Zhang

We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…

We give an $\alpha(1+\epsilon)$-approximation algorithm for solving covering LPs, assuming the presence of a $(1/\alpha)$-approximation algorithm for a certain optimization problem. Our algorithm is based on a simple modification of the…

Data Structures and Algorithms · Computer Science 2020-12-18 Eklavya Sharma

In a recent work, Esmer et al. describe a simple method - Approximate Monotone Local Search - to obtain exponential approximation algorithms from existing parameterized exact algorithms, polynomial-time approximation algorithms and, more…

Data Structures and Algorithms · Computer Science 2023-08-30 Baris Can Esmer , Ariel Kulik , Daniel Marx , Daniel Neuen , Roohani Sharma

A high number of discrete optimization problems, including Vertex Cover, Set Cover or Feedback Vertex Set, can be unified into the class of covering problems. Several of them were shown to be inapproximable by deterministic algorithms. This…

Data Structures and Algorithms · Computer Science 2013-05-14 Etienne Birmelé

We give logarithmic lower bounds for the approximability of the Minimum Dominating Set problem in connected (alpha,beta)-Power Law Graphs. We give also a best up to now upper approximation bound on the problem for the case of the parameters…

Computational Complexity · Computer Science 2012-12-17 Mikael Gast , Mathias Hauptmann , Marek Karpinski

In a Subgraph Problem we are given some graph and want to find a feasible subgraph that optimizes some measure. We consider Multistage Subgraph Problems (MSPs), where we are given a sequence of graph instances (stages) and are asked to find…

Data Structures and Algorithms · Computer Science 2023-06-16 Markus Chimani , Niklas Troost , Tilo Wiedera

We revisit the problem of designing sublinear algorithms for estimating the average degree of an $n$-vertex graph. The standard access model for graphs allows for the following queries: sampling a uniform random vertex, the degree of a…

Data Structures and Algorithms · Computer Science 2025-10-24 Lorenzo Beretta , Deeparnab Chakrabarty , C. Seshadhri

We consider the problem of partitioning the set of vertices of a given unit disk graph (UDG) into a minimum number of cliques. The problem is NP-hard and various constant factor approximations are known, with the current best ratio of 3.…

Computational Geometry · Computer Science 2015-05-13 Imran A. Pirwani , Mohammad R. Salavatipour

We study the minimum vertex cover problem in the following stochastic setting. Let $G$ be an arbitrary given graph, $p \in (0, 1]$ a parameter of the problem, and let $G_p$ be a random subgraph that includes each edge of $G$ independently…

Data Structures and Algorithms · Computer Science 2021-12-13 Soheil Behnezhad , Avrim Blum , Mahsa Derakhshan

In this paper we study the MAX-CUT problem on power law graphs (PLGs) with power law exponent $\beta$. We prove some new approximability results on that problem. In particular we show that there exist polynomial time approximation schemes…

Data Structures and Algorithms · Computer Science 2016-02-29 Mikael Gast , Mathias Hauptmann , Marek Karpinski

We present approximation algorithms with O(n^3) processing time for the minimum vertex and edge guard problems in simple polygons. It is improved from previous O(n^4) time algorithms of Ghosh. For simple polygon, there are O(n^3) visibility…

Computational Geometry · Computer Science 2015-03-17 Dae-Sung Jang , Sun-Il Kwon

This paper deals with the problem of finding a collection of vertex-disjoint paths in a given graph G=(V,E) such that each path has at least four vertices and the total number of vertices in these paths is maximized. The problem is NP-hard…

Data Structures and Algorithms · Computer Science 2023-04-26 Mingyang Gong , Zhi-Zhong Chen , Guohui Lin , Zhaohui Zhan

In this paper, we consider the problem of approximating the densest subgraph in the dynamic graph stream model. In this model of computation, the input graph is defined by an arbitrary sequence of edge insertions and deletions and the goal…

Data Structures and Algorithms · Computer Science 2015-06-16 Andrew McGregor , David Tench , Sofya Vorotnikova , Hoa T. Vu

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…

Data Structures and Algorithms · Computer Science 2013-11-05 Rajiv Gandhi , G. Kortsarz

Sublinear time algorithms for approximating maximum matching size have long been studied. Much of the progress over the last two decades on this problem has been on the algorithmic side. For instance, an algorithm of Behnezhad [FOCS'21]…

Data Structures and Algorithms · Computer Science 2022-11-30 Soheil Behnezhad , Mohammad Roghani , Aviad Rubinstein

A unit disk graph is the intersection graph of n congruent disks in the plane. Dominating sets in unit disk graphs are widely studied due to their application in wireless ad-hoc networks. Because the minimum dominating set problem for unit…

Data Structures and Algorithms · Computer Science 2014-02-07 Guilherme D. da Fonseca , Celina M. H. de Figueiredo , Vinícius G. P. de Sá , Raphael Machado