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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Achugbue, J. O., Chin, F.: Bounds on schedules for independent tasks with similar execution times. Journal of the ACM28, 1, 81–99 (1981).
Baker, R.: Introduction to sequencing and scheduling. New York: John Wiley 1974.
Coffman, E. G. Jr., Ed.: Computer and job/shop scheduling theory. New York: John Wiley 1976.
Coffman, E. G., Garey, M. R., Johnson, D. S.: An application of binpacking to multiprocessor scheduling. SIAM. J. Comput.7, 1, 1–17 (1978).
Graham, R. L.: Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math.17, 2, 416–429 (1969).
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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