Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Improved performance of the greedy algorithm for partial cover
Information Processing Letters
A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem
SIAM Journal on Discrete Mathematics
Generalized submodular cover problems and applications
Theoretical Computer Science
Using homogeneous weights for approximating the partial cover problem
Journal of Algorithms
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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
Dependent Rounding in Bipartite Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Covering Problems with Hard Capacities
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
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
Journal of Algorithms
Local ratio: A unified framework for approximation algorithms. In Memoriam: Shimon Even 1935-2004
ACM Computing Surveys (CSUR)
On the Equivalence between the Primal-Dual Schema and the Local Ratio Technique
SIAM Journal on Discrete Mathematics
A Primal-Dual Bicriteria Distributed Algorithm for Capacitated Vertex Cover
SIAM Journal on Computing
An improved approximation algorithm for vertex cover with hard capacities
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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
Parameterized complexity of generalized vertex cover problems
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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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 (or load) $\ell(e)$, and each vertex $v$ is associated with a (soft) 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 $\sum_{v}\alpha(v)w(v)$, where $\alpha(v)$ 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 the total demand of edges assigned to $v$ is at most $\alpha(v)c(v)$. 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. We also present 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.