An improved approximation algorithm for vertex cover with hard capacities (extended abstract)

Rajiv Gandhi; Eran Halperin; Samir Khuller; Guy Kortsarz; Aravind Srinivasan

doi:10.1007/3-540-45061-0_15

An improved approximation algorithm for vertex cover with hard capacities (extended abstract)

Rajiv Gandhi, Eran Halperin, Samir Khuller, Guy Kortsarz, Aravind Srinivasan

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

In this paper we study the capacitated vertex cover problem, a generalization of the well-known vertex cover problem. Given a graph G = (V, E), the goal is to cover all the edges by picking a minimum cover using the vertices. When we pick a vertex, we can cover up to a pre-specified number of edges incident on this vertex (its capacity). The problem is clearly NP-hard as it generalizes the well-known vertex cover problem. Previously, 2-approximation algorithms were developed with the assumption that multiple copies of a vertex may be chosen in the cover. If we are allowed to pick at most a given number of copies of each vertex, then the problem is significantly harder to solve. Chuzhoy and Naor (Proc. IEEE Symposium on Foundations of Computer Science, 481-489, 2002) have recently shown that the weighted version of this problem is at least as hard as set cover; they have also developed a 3-approximation algorithm for the unweighted version. We give a 2-approximation algorithm for the unweighted version, improving the Chuzhoy-Naor bound of 3 and matching (up to lower-order terms) the best approximation ratio known for the vertex cover problem.

Original language	English
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editors	Jos C. M. Baeten, Jan Karel Lenstra, Joachim Parrow, Gerhard J. Woeginger
Publisher	Springer Verlag
Pages	164-175
Number of pages	12
ISBN (Print)	3540404937, 9783540404934
DOIs	https://doi.org/10.1007/3-540-45061-0_15
State	Published - 2003
Externally published	Yes

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2719
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Keywords

Approximation algorithms
Capacitated covering
Linear programming
Randomized rounding
Set cover
Vertex cover

Access to Document

10.1007/3-540-45061-0_15

Cite this

Gandhi, R., Halperin, E., Khuller, S., Kortsarz, G., & Srinivasan, A. (2003). An improved approximation algorithm for vertex cover with hard capacities (extended abstract). In J. C. M. Baeten, J. K. Lenstra, J. Parrow, & G. J. Woeginger (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 164-175). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2719). Springer Verlag. https://doi.org/10.1007/3-540-45061-0_15

Gandhi, Rajiv ; Halperin, Eran ; Khuller, Samir et al. / An improved approximation algorithm for vertex cover with hard capacities (extended abstract). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). editor / Jos C. M. Baeten ; Jan Karel Lenstra ; Joachim Parrow ; Gerhard J. Woeginger. Springer Verlag, 2003. pp. 164-175 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "In this paper we study the capacitated vertex cover problem, a generalization of the well-known vertex cover problem. Given a graph G = (V, E), the goal is to cover all the edges by picking a minimum cover using the vertices. When we pick a vertex, we can cover up to a pre-specified number of edges incident on this vertex (its capacity). The problem is clearly NP-hard as it generalizes the well-known vertex cover problem. Previously, 2-approximation algorithms were developed with the assumption that multiple copies of a vertex may be chosen in the cover. If we are allowed to pick at most a given number of copies of each vertex, then the problem is significantly harder to solve. Chuzhoy and Naor (Proc. IEEE Symposium on Foundations of Computer Science, 481-489, 2002) have recently shown that the weighted version of this problem is at least as hard as set cover; they have also developed a 3-approximation algorithm for the unweighted version. We give a 2-approximation algorithm for the unweighted version, improving the Chuzhoy-Naor bound of 3 and matching (up to lower-order terms) the best approximation ratio known for the vertex cover problem.",

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Gandhi, R, Halperin, E, Khuller, S, Kortsarz, G & Srinivasan, A 2003, An improved approximation algorithm for vertex cover with hard capacities (extended abstract). in JCM Baeten, JK Lenstra, J Parrow & GJ Woeginger (eds), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2719, Springer Verlag, pp. 164-175. https://doi.org/10.1007/3-540-45061-0_15

An improved approximation algorithm for vertex cover with hard capacities (extended abstract). / Gandhi, Rajiv; Halperin, Eran; Khuller, Samir et al.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). ed. / Jos C. M. Baeten; Jan Karel Lenstra; Joachim Parrow; Gerhard J. Woeginger. Springer Verlag, 2003. p. 164-175 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2719).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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AU - Kortsarz, Guy

AU - Srinivasan, Aravind

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N2 - In this paper we study the capacitated vertex cover problem, a generalization of the well-known vertex cover problem. Given a graph G = (V, E), the goal is to cover all the edges by picking a minimum cover using the vertices. When we pick a vertex, we can cover up to a pre-specified number of edges incident on this vertex (its capacity). The problem is clearly NP-hard as it generalizes the well-known vertex cover problem. Previously, 2-approximation algorithms were developed with the assumption that multiple copies of a vertex may be chosen in the cover. If we are allowed to pick at most a given number of copies of each vertex, then the problem is significantly harder to solve. Chuzhoy and Naor (Proc. IEEE Symposium on Foundations of Computer Science, 481-489, 2002) have recently shown that the weighted version of this problem is at least as hard as set cover; they have also developed a 3-approximation algorithm for the unweighted version. We give a 2-approximation algorithm for the unweighted version, improving the Chuzhoy-Naor bound of 3 and matching (up to lower-order terms) the best approximation ratio known for the vertex cover problem.

AB - In this paper we study the capacitated vertex cover problem, a generalization of the well-known vertex cover problem. Given a graph G = (V, E), the goal is to cover all the edges by picking a minimum cover using the vertices. When we pick a vertex, we can cover up to a pre-specified number of edges incident on this vertex (its capacity). The problem is clearly NP-hard as it generalizes the well-known vertex cover problem. Previously, 2-approximation algorithms were developed with the assumption that multiple copies of a vertex may be chosen in the cover. If we are allowed to pick at most a given number of copies of each vertex, then the problem is significantly harder to solve. Chuzhoy and Naor (Proc. IEEE Symposium on Foundations of Computer Science, 481-489, 2002) have recently shown that the weighted version of this problem is at least as hard as set cover; they have also developed a 3-approximation algorithm for the unweighted version. We give a 2-approximation algorithm for the unweighted version, improving the Chuzhoy-Naor bound of 3 and matching (up to lower-order terms) the best approximation ratio known for the vertex cover problem.

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Gandhi R, Halperin E, Khuller S, Kortsarz G, Srinivasan A. An improved approximation algorithm for vertex cover with hard capacities (extended abstract). In Baeten JCM, Lenstra JK, Parrow J, Woeginger GJ, editors, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2003. p. 164-175. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45061-0_15

An improved approximation algorithm for vertex cover with hard capacities (extended abstract)

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