Refined memorization for vertex cover

Authors:
L. Sunil Chandran;Fabrizio Grandoni
Affiliations:
Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany;Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany
Venue:
Information Processing Letters
Year:
2005

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Abstract

Memorization is a technique which allows to speed up exponential recursive algorithms at the cost of an exponential space complexity. This technique already leads to the currently fastest algorithm for fixed-parameter vertex cover, whose time complexity is O(1.2832^kk^1^.^5+kn), where n is the number of nodes and k is the size of the vertex cover. Via a refined use of memorization, we obtain an O(1.2759^kk^1^.^5+kn) algorithm for the same problem. We moreover show how to further reduce the complexity to O(1.2745^kk^4+kn).