Comparability graph augmentation for some multiprocessor scheduling problems

P. Dell'Olmo, M. Grazia Speranza, Z. Tuza

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

A comparability graph is a graph which admits a transitive orientation. In this paper we consider the problem of augmenting a graph to a comparability graph in such a way that the maximum weight of its cliques is minimum. The problem is equivalent to a multiprocessor scheduling problem and to the interval coloring problem; and in the unweighted case also to the chromatic number problem. In the general case, the problem is NP-hard in the strong sense even on some very simple types of perfect graphs. We give complexity and approximation results for two subclasses of perfect graphs, namely for split graphs and stars of cliques, for which the problem still remains intractable but admits efficient estimations.

Original languageEnglish
Pages (from-to)71-84
Number of pages14
JournalDiscrete Applied Mathematics
Volume72
Issue number1-2
Publication statusPublished - Jan 10 1997

Fingerprint

Comparability Graph
Multiprocessor Scheduling
Augmentation
Coloring
Stars
Scheduling Problem
Computational complexity
Scheduling
Perfect Graphs
Clique
Split Graph
Efficient Estimation
Graph in graph theory
Chromatic number
Colouring
Star
NP-complete problem
Interval
Approximation

Keywords

  • Approximation results
  • Comparability graphs
  • Computational complexity
  • Interval coloring
  • Multiprocessor scheduling
  • Split graphs

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Comparability graph augmentation for some multiprocessor scheduling problems. / Dell'Olmo, P.; Speranza, M. Grazia; Tuza, Z.

In: Discrete Applied Mathematics, Vol. 72, No. 1-2, 10.01.1997, p. 71-84.

Research output: Contribution to journalArticle

Dell'Olmo, P. ; Speranza, M. Grazia ; Tuza, Z. / Comparability graph augmentation for some multiprocessor scheduling problems. In: Discrete Applied Mathematics. 1997 ; Vol. 72, No. 1-2. pp. 71-84.
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