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

Sounaka Mishra; Kripasindhu Sikdar

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 35, Issue: 3, page 287-309
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Mishra, Sounaka, and Sikdar, Kripasindhu. "On the Hardness of Approximating Some NP-optimization Problems Related to Minimum Linear Ordering Problem." RAIRO - Theoretical Informatics and Applications 35.3 (2010): 287-309. <http://eudml.org/doc/222064>.

@article{Mishra2010,
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. },
author = {Mishra, Sounaka, Sikdar, Kripasindhu},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {NP-optimization problems; Minimaximal and maximinimal NP-opt- imization problems; Approximation algorithms; Hardness of approximation; APX-hardness; AP-reduction; L-reduction; S-reduction.; minimum linear ordering problem},
language = {eng},
month = {3},
number = {3},
pages = {287-309},
publisher = {EDP Sciences},
title = {On the Hardness of Approximating Some NP-optimization Problems Related to Minimum Linear Ordering Problem},
url = {http://eudml.org/doc/222064},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Mishra, Sounaka
AU - Sikdar, Kripasindhu
TI - On the Hardness of Approximating Some NP-optimization Problems Related to Minimum Linear Ordering Problem
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 3
SP - 287
EP - 309
AB - 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.
LA - eng
KW - NP-optimization problems; Minimaximal and maximinimal NP-opt- imization problems; Approximation algorithms; Hardness of approximation; APX-hardness; AP-reduction; L-reduction; S-reduction.; minimum linear ordering problem
UR - http://eudml.org/doc/222064
ER -

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