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Efficiently solvable special cases of hard combinatorial optimization problems

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Abstract

We survey some recent advances in the field of polynomially solvable special cases of hard combinatorial optimization problems like the travelling salesman problem, quadratic assignment problems and Steiner tree problems. Such special cases can be found by considering special cost structures, the geometry of the problem, the special topology of the underlying graph structure or by analyzing special algorithms. In particular we stress the importance of recognition algorithms. We comment on open problems in this area and outline some lines for future research in this field.

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Authors and Affiliations

  1. Institut für Mathematik B, TU Graz, Steyrergasse 30, A-8010, Graz, Austria

    Rainer E. Burkard

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  1. Rainer E. Burkard
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This research has been supported by the Spezialforschungsbereich F 003 “Optimierung und Kontrolle”, Projektbereich Diskrete Optimierung.

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Burkard, R.E. Efficiently solvable special cases of hard combinatorial optimization problems. Mathematical Programming 79, 55–69 (1997). https://doi.org/10.1007/BF02614311

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