# On the hardness of approximating some NP-optimization problems related to minimum linear ordering problem

Sounaka Mishra; Kripasindhu Sikdar

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2001)

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

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topMishra, Sounaka, and Sikdar, Kripasindhu. "On the hardness of approximating some NP-optimization problems related to minimum linear ordering problem." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 35.3 (2001): 287-309. <http://eudml.org/doc/92667>.

@article{Mishra2001,

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 - Informatique Théorique et Applications},

keywords = {NP-optimization problems; minimaximal and maximinimal NP-optimization problems; approximation algorithms; hardness of approximation; APX-hardness; AP-reduction; L-reduction; S-reduction; minimum linear ordering problem},

language = {eng},

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/92667},

volume = {35},

year = {2001},

}

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 - Informatique Théorique et Applications

PY - 2001

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-optimization problems; approximation algorithms; hardness of approximation; APX-hardness; AP-reduction; L-reduction; S-reduction; minimum linear ordering problem

UR - http://eudml.org/doc/92667

ER -

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