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On the Hardness of Approximating Some NP-optimization Problems Related to Minimum Linear Ordering Problem

Published online by Cambridge University Press:  15 April 2002

Sounaka Mishra  and
Kripasindhu Sikdar
Sounaka Mishra
Affiliation:
Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Calcutta 700 035, India; e-mail: res9513@isical.ac.in
Kripasindhu Sikdar
Affiliation:
Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Calcutta 700 035, India; e-mail: sikdar@isical.ac.in
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Abstract

We study hardness of approximating several minimaximal and maximinimal NP-optimization problems related to the minimum linear ordering problem (MINLOP). MINLOP is to find a minimum weight acyclic tournament in a given arc-weighted complete digraph. MINLOP is APX-hard but its unweighted version is polynomial time solvable. We prove that MIN-MAX-SUBDAG problem, which is a generalization of MINLOP and requires to find a minimum cardinality maximal acyclic subdigraph of a given digraph, is, however, APX-hard. Using results of Håstad concerning hardness of approximating independence number of a graph we then prove similar results concerning MAX-MIN-VC (respectively, MAX-MIN-FVS) which requires to find a maximum cardinality minimal vertex cover in a given graph (respectively, a maximum cardinality minimal feedback vertex set in a given digraph). We also prove APX-hardness of these and several related problems on various degree bounded graphs and digraphs.

Keywords

NP-optimization problemsMinimaximal and maximinimal NP-opt- imization problemsApproximation algorithmsHardness of approximationAPX-hardnessAP-reductionL-reductionS-reduction.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 35 , Issue 3 , May 2001 , pp. 287 - 309
Copyright
© EDP Sciences, 2001

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