DMCA
Combinatorial optimization with explicit delineation of the ground set by a collection of subsets (2008)
| Venue: | In SIAM J. Discrete Math |
| Citations: | 6 - 0 self |
BibTeX
@ARTICLE{Dror08combinatorialoptimization,
author = {Moshe Dror and James B. Orlin},
title = {Combinatorial optimization with explicit delineation of the ground set by a collection of subsets},
journal = {In SIAM J. Discrete Math},
year = {2008},
pages = {1019--1034}
}
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Abstract
We examine a selective list of combinatorial optimization problems in NP with respect to inapproximability (Arora and Lund, 1997) given that the ground set of elements N has additional characteristics. For each problem in this paper, the set N is expressed explicitly by subsets of N either as a partition or in the form of a cover. The problems examined are generalizations of well known classical graph problems and include the minimal spanning tree, the assignment problem, a number of elementary machine scheduling problems, bin-packing, and the TSP. We conclude that for all these generalized problems the existence of PTAS (polynomial time approximation scheme) is impossible unless P=NP. This suggests a partial characterization for a family of inapproximable problems. For the generalized Euclidean TSP we prove inapproximability even if the subsets are of cardinality two.
Keyphrases
combinatorial optimization explicit delineation inapproximable problem elementary machine scheduling problem ground set additional characteristic polynomial time approximation scheme partial characterization combinatorial optimization problem classical graph problem minimal spanning tree assignment problem selective list generalized euclidean tsp
