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Reports (Research Report) Year : 1992

Combinatorial optimization problems for which almost every algorithm is asymptotically optimal

Wojciec Szpankowski
  • Function : Author

Abstract

Let Zmax and Zmin be respectively the maximum and minimum of the objective function in a combinatorial problem for which the cardinality of the set of feasible solutions is m and the size of every feasible solution is N. We prove that in a certain probabilistic framework Zmax ~ Zmin almost surely (a.s.) provided log m = o (N) for N and m become large. This result implies that for such a class of combinatorial optimization probblems almost every algorithm finds asymptotically optimal solution. The quadratic assignment problem, the location problem on graphs, and some pattern matching problems fall into this class.

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Other [cs.OH]
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Dates and versions

inria-00077010 , version 1 (29-05-2006)

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  • HAL Id : inria-00077010 , version 1

Cite

Wojciec Szpankowski. Combinatorial optimization problems for which almost every algorithm is asymptotically optimal. [Research Report] RR-1770, INRIA. 1992. ⟨inria-00077010⟩
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