Combinational optimization problems for which almost every algorithm is asymptotically optimal

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 as N and m become large. This result implies that for such a class of combinatorial optimization problems almost ecery algorithm finds asymptotically optimal solution! The quadratic assignment problem, a location problem on graphs, and a pattern matching problem fall into this class