Counting and enumeration complexity with application to multicriteria scheduling

Counting and enumeration complexity with application to multicriteria scheduling

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Article ID: iaor20083015
Country: Netherlands
Volume: 153
Issue: 1
Start Page Number: 215
End Page Number: 234
Publication Date: Sep 2007
Journal: Annals of Operations Research
Authors: , ,
Abstract:

In this paper we tackle an important point of combinatorial optimisation: that of complexity theory when dealing with the counting or enumeration of optimal solutions. Complexity theory has been initially designed for decision problems and evolved over the years, for instance, to tackle particular features in optimisation problems. It has also evolved, more or less recently, towards the complexity of counting and enumeration problems and several complexity classes, which we review in this paper, have emerged in the literature. This kind of problems makes sense, notably, in the case of multicriteria optimisation where the aim is often to enumerate the set of the so-called Pareto optima. In the second part of this paper we review the complexity of multicriteria scheduling problems in the light of the previous complexity results.

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