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The asymptotic probabilistic behaviour of quadratic sum assignment problems

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  • Series A: Theory
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Abstract

In this paper a surprising probabilistic behaviour of quadratic sum assignment problems is shown. The relative difference between worst and optimal solution value tends to zero with probability tending to one as the size of the problem goes to infinity. This result suggests that for high dimensional quadratic assignment problems even very simple approximation algorithms can in practice yield good suboptimal solutions.

Zusammenfassung

In dieser Arbeit wird ein überraschendes asymptotisches Verhalten von quadratischen Zuordnungsproblemen mit Summenzielfunktion aufgezeigt. Es wird bewiesen, daß der relative Unterschied zwischen schlechtestem und bestem Zielfunktionswert mit Wahrscheinlichkeit gegen 1 nach Null strebt, wenn die Dimension der Probleme gegen Unendlich geht. Aufgrund dieses Resultates kann man erwarten, daß schon sehr einfache Heuristiken für höher-dimensionale Probleme in der Praxis recht gute Näherungslösungen liefern.

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Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Graz, Kopernikusgasse 24, A-8010, Graz

    R. E. Burkard

  2. Mainzerstr. 41, D-5000, Köln 1

    U. Fincke Dipl. Math.

Authors
  1. R. E. Burkard
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  2. U. Fincke Dipl. Math.
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Burkard, R.E., Fincke, U. The asymptotic probabilistic behaviour of quadratic sum assignment problems. Zeitschrift für Operations Research 27, 73–81 (1983). https://doi.org/10.1007/BF01916903

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  • DOI: https://doi.org/10.1007/BF01916903

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