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Some results in chromatic scheduling

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Summary

Ap-boundedk-coloration of a multigraphG is a partition of its edges into subsetsS 1,…,S k such that ¦s i (x)}-s j (x)}⩽p fori,j=1,…,k and for any nodex. Heres j (x) is the number of edges ins j which are adjacent to nodex.

This type of coloration is also defined for hypergraphs. Some properties of these colorations are established and their applications to a few scheduling problems (in particular to school timetabling) are discussed.

Zusammenfassung

Einep-gebundenek-Kolorierung eines MultigraphsG ist eine Aufteilung seiner Kanten in UntermengenS 1,…,S k in der Weise, daß ¦s i (x)}-s j (x)¦⩽p ist für allei,j=1,…,k und für jeden Knotenx. Hierbei ists j (x) die Zahl der zum Knotenx benachbarten Kanten in Sj.

Diese Art der Kolorierung wird auch für Hypergraphen definiert. Außerdem werden verschiedene Eigenschaften dieser Kolorierungen entwickelt und ihre Anwendungen auf einige Zuordnungs- bzw. Terminplanungsprobleme (insbesondere auf Schulstundenpläne) diskutiert.

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References

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  • McDiarmid, C. J. H.: The Solution of a Timetabling Problem, in: J. Inst. Maths. Applics.,9, 23–34, 1972.

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Authors and Affiliations

  1. Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, 26, av. de Cour, CH-1007, Lausanne, Suisse

    D. de Werra

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  1. D. de Werra
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de Werra, D. Some results in chromatic scheduling. Zeitschrift für Operations Research 18, 167–175 (1974). https://doi.org/10.1007/BF02026597

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  • DOI: https://doi.org/10.1007/BF02026597

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