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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... (Update)
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BibTeX entry: (Update)
W. Szpankowski, Combinatorial optimization problems for which almost every algorithm is asymptotically optimal, Optimization, 33, 359-368, 1995. http://citeseer.ist.psu.edu/szpankowski94combinatorial.html More
@techreport{ szpankowskiszpankowskicombinatorial,
author = "Wojciec Szpankowski",
title = "Combinatorial optimization problems for which almost every algorithm is asymptotically optimal",
number = "RR-1770",
pages = "9 p.",
url = "citeseer.ist.psu.edu/szpankowski94combinatorial.html" }
Citations (may not include all citations):1749 An Introduction to Probability Theory and its Applications (context) - Feller - 1971
602 Convergence of Probability Measures (context) - Billingsley - 1968
22 Worst-Case and Probabilistic Analysis of a Geometric Locatio.. (context) - Papadimitriou - 1981
10 Probabilistic Asymptotic properties of some Combinatorial Op.. (context) - Burkard, Fincke - 1985
9 On Linear Programs with Random Costs (context) - Dyer, Frieze et al. - 1986
7 A Note on Asymptotic Properties of the Quadratic Assignment .. (context) - Rhee - 1988
6 for Coin Tossing and Sequence Matching (context) - Arratia, Gordon et al. - 1990
4 Maximum Size of a Dynamic Data Structure: Hashing With Lazy .. - Aldous, Hofri et al. - 1992
4 Asymptotic Properties of the Quadratic Assignment Problem (context) - Frenk, van Houweninge et al. - 1985
4 Optimization Problems on Graphs with Independent Random Edge.. (context) - Lueker - 1981
1 Random Graphs and Graph Optimization Problems (context) - Weide - 1980
1 Combinatorial optimization through order statistics (context) - Szpankowski - 1991
1 Pattern Matching with Mismatches: A Randomized Algorithm and.. (context) - Atallah, Jacquet et al. - 1993
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