A Primal-Dual Approximation Algorithm for Partial Vertex Cover: Making Educated Guesses

We study the partial vertex cover problem. Given a graph G =( V , E ), a weight function w : V → R + , and an integer s , our goal is to cover all but s edges, by picking a set of vertices with minimum weight. The problem is clearly NP-hard as it generalizes the well-known vertex cover problem. We p...

Full description

Saved in:
Bibliographic Details
Published in:Algorithmica Vol. 55; no. 1; pp. 227 - 239
Main Author: Mestre, Julián
Format: Journal Article Conference Proceeding
Language:English
Published: New York Springer-Verlag 01.09.2009
Springer
Subjects:
Algorithm Analysis and Problem Complexity
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Computer Science
Computer science; control theory; systems
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Exact sciences and technology
Mathematics of Computing
Theoretical computing
Theory of Computation
Vertex cover
Approximation algorithms
Primal-dual algorithms
Weight function
Primal dual method
NP hard problem
Graph covering
Approximation algorithm
Orientation
ISSN:0178-4617, 1432-0541
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study the partial vertex cover problem. Given a graph G =( V , E ), a weight function w : V → R + , and an integer s , our goal is to cover all but s edges, by picking a set of vertices with minimum weight. The problem is clearly NP-hard as it generalizes the well-known vertex cover problem. We provide a primal-dual 2-approximation algorithm which runs in O ( n log  n + m ) time. This represents an improvement in running time from the previously known fastest algorithm. Our technique can also be used to get a 2-approximation for a more general version of the problem. In the partial capacitated vertex cover problem each vertex u comes with a capacity k u . A solution consists of a function x : V →ℕ 0 and an orientation of all but s edges, such that the number of edges oriented toward vertex u is at most x u k u . Our objective is to find a cover that minimizes ∑ v ∈ V x v w v . This is the first 2-approximation for the problem and also runs in O ( n log  n + m ) time.
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-007-9003-z