Scheduling precedence graphs of bounded height

Danny Dolev; Manfred K. Warmuth

doi:10.1016/0196-6774(84)90039-7

Scheduling precedence graphs of bounded height

Danny Dolev^*
, Manfred K. Warmuth

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

35 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 language	English
Pages (from-to)	48-59
Number of pages	12
Journal	Journal of Algorithms
Volume	5
Issue number	1
DOIs	https://doi.org/10.1016/0196-6774(84)90039-7
State	Published - Mar 1984
Externally published	Yes

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title = "Scheduling precedence graphs of bounded height",

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.",

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Scheduling precedence graphs of bounded height

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