Fixed-Parameter Evolutionary Algorithms and the Vertex Cover Problem
نویسندگان
چکیده
منابع مشابه
On Efficient Fixed Parameter Algorithms for WEIGHTED VERTEX COVER
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, Weighted 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 t...
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This paper reports work investigating various evolutionary approaches to vertex cover (VC), a well-known NP-Hard optimization problem. Central to each of the algorithms is a novel encoding scheme for VC and related problems that treats each chromosome as a binary decision diagram. As a result, the encoding allows only a (guaranteed optimal) subset of feasible solutions. The encoding also incorp...
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The VERTEX COVER problem asks, for input consisting of a graph G on n vertices, and a positive integer k, whether there is a set of k vertices such that every edge of G is incident with at least one of these vertices. We give an algorithm for this problem that runs in time O(kn + (1.324718)'k'). In particular, this gives an 0((1.324718) " n2) algorithm to find the minimum vertex cover in the gr...
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A rigorous runtime analysis of evolutionary multi-objective optimization for the classical vertex cover problem in the context of parameterized complexity analysis has been presented by Kratsch and Neumann [11]. In this paper, we extend the analysis to the weighted vertex cover problem and provide a fixed parameter evolutionary algorithm with respect to OPT , where OPT is the cost of the the op...
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Our goal in this paper is the development of fast algorithms for recognizing general classes of graphs. We seek algorithms whose complexity can be expressed as a linear function of the graph size plus an exponential function of k, a natural parameter describing the class. In particular, we consider the class Wk(G), where for each graph G in Wk(G), the removal of a set of at most k vertices from...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2012
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-012-9660-4