TY - GEN

T1 - Improved approximation algorithms for the partial vertex cover problem

AU - Halperin, Eran

AU - Srinivasan, Aravind

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.

PY - 2002

Y1 - 2002

N2 - The partial vertex cover problemis a generalization of the vertex cover problem: given an undirected graph G = (V,E) and an integer k, we wish to choose a minimum number of vertices such that at least k edges are covered. Just as for vertex cover, 2-approximation algorithms are known for this problem, and it is of interest to see if we can do better than this. The current-best approximation ratio for partial vertex cover, when parameterized by the maximum degree d of G, is (2−Θ(1/d)). We improve on this by presenting a (formula presented)-approximation algorithm for partial vertex cover using semidefinite programming, matching the current-best bound for vertex cover. Our algorithmuses a new rounding technique, which involves a delicate probabilistic analysis.

AB - The partial vertex cover problemis a generalization of the vertex cover problem: given an undirected graph G = (V,E) and an integer k, we wish to choose a minimum number of vertices such that at least k edges are covered. Just as for vertex cover, 2-approximation algorithms are known for this problem, and it is of interest to see if we can do better than this. The current-best approximation ratio for partial vertex cover, when parameterized by the maximum degree d of G, is (2−Θ(1/d)). We improve on this by presenting a (formula presented)-approximation algorithm for partial vertex cover using semidefinite programming, matching the current-best bound for vertex cover. Our algorithmuses a new rounding technique, which involves a delicate probabilistic analysis.

KW - Approximation algorithms

KW - Partial vertex cover

KW - Randomized rounding

KW - Semidefinite programming

UR - http://www.scopus.com/inward/record.url?scp=84956970098&partnerID=8YFLogxK

U2 - 10.1007/3-540-45753-4_15

DO - 10.1007/3-540-45753-4_15

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AN - SCOPUS:84956970098

SN - 3540441867

SN - 9783540441861

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 161

EP - 174

BT - Approximation Algorithms for Combinatorial Optimization - 5th International Workshop, APPROX 2002, Proceedings

A2 - Jansen, Klaus

A2 - Leonardi, Stefano

A2 - Vazirani, Vijay

PB - Springer Verlag

T2 - 5th International Workshop On Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2002

Y2 - 17 September 2002 through 21 September 2002

ER -