Asymptotically Optimal Heuristics for Bottleneck and Capacity Optimization Problems

Our goal is to design simple and asymptotically optimal heuristic algorithms for a class of bottleneck and capacity optimization problems. Our approach is applied to a wide variety of bottleneck problems including vehicle routing problems, location problems, and communication network problems. In particular, we present simple and asymptotically optimal heuristic algorithms that solve the bottleneck assignment problem, the bottleneck spanning tree problem and the directed bottleneck traveling salesman problem in O(n 2 ) with high probability (our algorithm runs in O(n3+e ) for the undirected version of the bottleneck traveling salesman problem). In addition, we extend our results to the d-th best solution for some bottleneck optimization problems. "This research was supported in part by the NSF grants CCR-8900305 (its extension CCR-9201078), and NCR-9206315 and INT-8912631, in part by AFOSR grant 90-0107, and by NATO Collaborative Grant 0057/89, and by Grant R01 LM05118 from the National Library of Medicine. This paper was revised while the author was visiting INRIA, Rocquencourt, France, and he wishes to thank INRIA (projects ALGa, MEVAL and REFLECS) for a generous support.