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• W2071463666 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." @default.
• W2071463666 created "2016-06-24" @default.
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• W2071463666 date "2001-05-01" @default.
• W2071463666 modified "2023-09-24" @default.
• W2071463666 title "On the Hardness of Approximating Some NP-optimization Problems Related to Minimum Linear Ordering Problem" @default.
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• W2071463666 doi "https://doi.org/10.1051/ita:2001121" @default.
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