Combinatorial Optimization Problems For Which Almost Every Algorithm Is Asymptotically Optimal! (1994)
| Venue: | Optimization |
| Citations: | 11 - 1 self |
BibTeX
@INPROCEEDINGS{Szpankowski94combinatorialoptimization,
author = {Wojciech Szpankowski},
title = {Combinatorial Optimization Problems For Which Almost Every Algorithm Is Asymptotically Optimal!},
booktitle = {Optimization},
year = {1994},
pages = {359--367}
}
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
Consider a class of optimization problems for which the cardinality of the set of feasible solutions is m and the size of every feasible solution is N . We prove in a general probabilistic framework that the value of the optimal solution and the value of the worst solution are asymptotically almost surely (a.s.) the same provided log m = o(N) as N and m become large. This result implies that for such a class of combinatorial optimization problems almost every algorithm finds asymptotically optimal solution! The quadratic assignment problem, the location problem on graphs, and a pattern matching problem fall into this class. This research was primary done while the author was visiting INRIA, Rocquencourt, France, and he wishes to thank INRIA (projects ALGO, MEVAL and REFLECS) for a generous support. In addition, support was provided by NSF Grants CCR-9201078, NCR-9206315 and INT-8912631, by Grant AFOSR-90-0107, and in part by NATO Collaborative Grant 0057/89. 1. INTRODUCTION We co...
