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.
@article{ITA_2001__35_3_287_0,
author = {Mishra, Sounaka and Sikdar, Kripasindhu},
title = {On the hardness of approximating some NP-optimization problems related to minimum linear ordering problem},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
volume = {35},
year = {2001},
pages = {287-309},
mrnumber = {1869219},
zbl = {1014.68063},
language = {en},
url = {http://dml.mathdoc.fr/item/ITA_2001__35_3_287_0}
}
Mishra, Sounaka; 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, Tome 35 (2001) pp. 287-309. http://gdmltest.u-ga.fr/item/ITA_2001__35_3_287_0/
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