Scheduling precedence graphs of bounded height

Danny Dolev*, Manfred K. Warmuth

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

The existence of a schedule for a partially ordered set of unit length tasks on m identical processors is known to be NP-complete (J. D. Ullman, NP-complete scheduling problems, J. Comput. System Sci., 10 (1975), 384-393). The problem remains NP-complete even if we restrict the precedence graph to be of height bounded by a constant. (J. K. Lenkstra and A. H. G. Rinnooy Kan, Complexity of scheduling under precedence constraints, Operations Res., 26 (1978), 22-35; D. Dolev and M. K. Warmuth, "Scheduling Flat Graphs," IBM Research Report RJ 3398, 1982). In these NP-completeness proofs the upper bound on the number of available processors varies with the problem instance. We present a polynomial algorithm for the case where the upper bound on the number of available processors and the height of the precedence graph are both constants.

Original languageEnglish
Pages (from-to)48-59
Number of pages12
JournalJournal of Algorithms
Volume5
Issue number1
DOIs
StatePublished - Mar 1984
Externally publishedYes

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