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Recognizing when heuristics can approximate minimum vertex covers is complete for parallel access to NP

Published online by Cambridge University Press:  15 October 2005

Edith Hemaspaandra ,
Jörg Rothe  and
Holger Spakowski
Edith Hemaspaandra
Affiliation:
Department of Computer Science, Rochester Institute of Technology, Rochester, NY 14623, USA; eh@cs.rit.edu
Jörg Rothe
Affiliation:
Institut für Informatik, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany; rothe@cs.uni-duesseldorf.de; spakowsk@cs.uni-duesseldorf.de
Holger Spakowski
Affiliation:
Institut für Informatik, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany; rothe@cs.uni-duesseldorf.de; spakowsk@cs.uni-duesseldorf.de
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Abstract

For both the edge deletion heuristic and the maximum-degree greedy heuristic, we studythe problem of recognizing those graphs for which that heuristic can approximate the size of a minimum vertex cover within a constant factor of r, where r is a fixed rational number. Our main results are that these problems are complete for the class of problems solvable via parallel access to NP. To achieve these main results, we also show that the restriction of the vertex cover problem to those graphs for which either of these heuristics can find an optimal solution remains NP-hard.

Keywords

Computational complexitycompletenessminimum vertex cover heuristicsapproximationparallel access to NP
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 40 , Issue 1 , January 2006 , pp. 75 - 91
Copyright
© EDP Sciences, 2006

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