Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
A survey of approximately optimal solutions to some covering and packing problems
ACM Computing Surveys (CSUR)
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
An improved fixed-parameter algorithm for vertex cover
Information Processing Letters
How to find the best approximation results
ACM SIGACT News
A general method to speed up fixed-parameter-tractable algorithms
Information Processing Letters
New upper bounds for maximum satisfiability
Journal of Algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
New Worst-Case Upper Bounds for SAT
Journal of Automated Reasoning
An Efficient Exact Algorithm for Constraint Bipartite Vertex Cover
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
Fixed Parameter Algorithms for PLANAR DOMINATING SET and Related Problems
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Deterministic Algorithms for k-SAT Based on Covering Codes and Local Search
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Upper Bounds for MaxSat: Further Improved
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
An efficient fixed-parameter algorithm for 3-hitting set
Journal of Discrete Algorithms
Worst-case upper bounds for MAX-2-SAT with an application to MAX-CUT
Discrete Applied Mathematics - The renesse issue on satisfiability
Upper bounds for vertex cover further improved
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Parameterized Complexity
Minimum Quartet Inconsistency Is Fixed Parameter Tractable
CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
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We investigate the fixed parameter complexity of one of the most popular problems in combinatorial optimization, WEIGHTED VERTEX COVER. Given a graph G = (V, E), a weight function ω: V → R+, and k ∈ R+, WEIGHETD VERTEX COVER (WVC for short) asks for a subset C of vertices in V of weight at most k such that every edge of G has at least one endpoint in C. WVC and its variants have all been shown to be NP-complete. We show that, when restricting the range of ω to positive integers, the so-called INTEGER-WVC can be solved as fast as unweighted VERTEX COVER. Our main result is that if the range of ω is restricted to positive reals ≥ 1, then so-called REAL-WVC can be solved in time O(1.3954k + k|V|). If we modify the problem in such a way that k is not the weight of the vertex cover we are looking for, but the number of vertices in a minimum weight vertex cover, then the same running time can be obtained. If the weights are arbitrary (referred to by GENERAL-WVC), however, the problem is not fixed parameter tractable unless P = NP.