@inbook{41c7883dcbff4682978e76c619a72221,

title = "An improved approximation algorithm for vertex cover with hard capacities (extended abstract)",

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.",

keywords = "Approximation algorithms, Capacitated covering, Linear programming, Randomized rounding, Set cover, Vertex cover",

author = "Rajiv Gandhi and Eran Halperin and Samir Khuller and Guy Kortsarz and Aravind Srinivasan",

year = "2003",

doi = "10.1007/3-540-45061-0_15",

language = "אנגלית",

isbn = "3540404937",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "164--175",

editor = "Baeten, {Jos C. M.} and Lenstra, {Jan Karel} and Joachim Parrow and Woeginger, {Gerhard J.}",

booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

}