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 problems, minimaximal and maximinimal NP-optimization problems, approximation algorithms, hardness of approximation, APX-hardness, AP-reduction, L-reduction, S-reduction

@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}, pages = {287--309}, publisher = {EDP-Sciences}, volume = {35}, number = {3}, year = {2001}, zbl = {1014.68063}, mrnumber = {1869219}, language = {en}, url = {http://www.numdam.org/item/ITA_2001__35_3_287_0/} }

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 DA - 2001/// SP - 287 EP - 309 VL - 35 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/item/ITA_2001__35_3_287_0/ UR - https://zbmath.org/?q=an%3A1014.68063 UR - https://www.ams.org/mathscinet-getitem?mr=1869219 LA - en ID - ITA_2001__35_3_287_0 ER -

%0 Journal Article %A Mishra, Sounaka %A Sikdar, Kripasindhu %T On the hardness of approximating some NP-optimization problems related to minimum linear ordering problem %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2001 %P 287-309 %V 35 %N 3 %I EDP-Sciences %G en %F 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, Volume 35 (2001) no. 3, pp. 287-309. http://www.numdam.org/item/ITA_2001__35_3_287_0/

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