Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
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Information Processing Letters
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STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Computational Complexity of Machine Learning
Computational Complexity of Machine Learning
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STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Improved Approximation Algorithms for the Partial Vertex Cover Problem
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Distributions on Level-Sets with Applications to Approximation Algorithms
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Approximation algorithms for partial covering problems
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Local ratio: A unified framework for approximation algorithms. In Memoriam: Shimon Even 1935-2004
ACM Computing Surveys (CSUR)
Dependent rounding and its applications to approximation algorithms
Journal of the ACM (JACM)
An improved approximation algorithm for vertex cover with hard capacities
Journal of Computer and System Sciences
A primal-dual approximation algorithm for partial vertex cover: making educated guesses
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Set cover revisited: hypergraph cover with hard capacities
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Journal of Discrete Algorithms
Analytical models for risk-based intrusion response
Computer Networks: The International Journal of Computer and Telecommunications Networking
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We study the partial capacitated vertex cover problem (pcvc) in which the input consists of a graph G and a covering requirement L. Each edge e in G is associated with a demand l(e), and each vertex v is associated with a capacity c(v) and a weight w(v). A feasible solution is an assignment of edges to vertices such that the total demand of assigned edges is at least L. The weight of a solution is Σv α(v)w(v), where α(v) is the number of copies of v required to cover the demand of the edges that are assigned to v. The goal is to find a solution of minimum weight. We consider three variants of pcvc. In pcvc with separable demands the only requirement is that total demand of edges assigned to v is at most α(v)c(v). In pcvc with inseparable demands there is an additional requirement that if an edge is assigned to v then it must be assigned to one of its copies. The third variant is the unit demands version. We present 3-approximation algorithms for both pcvc with separable demands and pcvc with inseparable demands and a 2-approximation algorithm for pcvc with unit demands. We show that similar results can be obtained for pcvc in hypergraphs and for the prize collecting version of capacitated vertex cover. Our algorithms are based on a unified approach for designing and analyzing approximation algorithms for capacitated covering problems. This approach yields simple algorithms whose analyses rely on the local ratio technique and sophisticated charging schemes.