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Bounds for nonpreemptive scheduling of jobs with similar processing times on multiprocessor systems using the LPT-Algorithm

Schranken für das Scheduling ohne Unterbrechung von Jobs mit ähnlichen Prozeßzeiten auf einem Multiprozessorsystem unter Verwendung des LPT-Algorithmus

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Abstract

The well-known, NP-complete problem of scheduling a set ofn independent jobs nonpreemptively onm identical parallel processors to minimize the maximum finish time is considered. Let ω0 be the finish time of an optimal schedule and ω the finish time of a schedule found by the Longest Processing Time (LPT-)heuristic. We will improve the Graham-bound for the LPT-heuristic (ω/ω0 ≤ 4/3 − 1/3m) which is tight in general, by considering only jobs with similar processing times.

Zusammenfassung

Wir untersuchen das bekannte, NP-vollständige Problem des Scheduling einer Menge vonn unabhängigen Jobs ohne Unterbrechung aufm identischen parallelen Maschinen um die maximale Fertigstellungszeit zu minimieren. Sei ω0 die Fertigstellungszeit eines optimalen Schedule und ω die Fertigstellungszeit des Schedule, den man durch die LPT-Heuristik erhält. Wir verbessern die Graham-Schranke für die LPT-Heuristik (ω/ω0 ≤ 4/3 − 1/3m), eine im allgemeinen Fall scharfe Schranke, indem wir nur Jobs mit ähnlichen Prozeßzeiten untersuchen.

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Research partially supported by the Austrian Science Foundation (Fonds zur Förderung der wissenschaftlichen Forschung), project S32/01.

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Kellerer, H. Bounds for nonpreemptive scheduling of jobs with similar processing times on multiprocessor systems using the LPT-Algorithm. Computing 46, 183–191 (1991). https://doi.org/10.1007/BF02238297

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  • DOI: https://doi.org/10.1007/BF02238297

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