Combinatorial optimization with explicit delineation of the ground set by a collection of subsets

Moshe Dror, James B. Orlin

Research output: Contribution to journalArticle

11 Scopus citations

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 problem, a number of elementary machine scheduling problems, the bin-packing problem, and the travelling salesman problem (TSP). We conclude that for all these generalized problems the existence of a polynomial time approximation scheme (PTAS) 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 2.

Original languageEnglish (US)
Pages (from-to)1019-1034
Number of pages16
JournalSIAM Journal on Discrete Mathematics
Volume21
Issue number4
DOIs
StatePublished - Dec 1 2007

Keywords

  • Approximation algorithms
  • Generalized bin packing
  • Generalized scheduling problems
  • Inapproximability
  • Subset travelling salesman

ASJC Scopus subject areas

  • Mathematics(all)

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