Another Unified Approach to Some Bottleneck and Capacity Optimization Problems

The purpose of this paper is twofold. Namely, to present a probabilistic analysis of a class of bottleneck (capacity) optimization problems, and to design simple and efficient heuristic algorithms guaranteed to be asymptotically optimal. OUf unified approach is applied to a wide variety of bottleneck problems including vehicle routing problems, location problems, and communication network problems. In particular, we present a simple and a.symptotically optimal heuristic algorithms that solve the bottleneck assignment problem, the bottleneck spanning tree problem and the directed bottleneck traveling salesman problem in O(n2) time-complexity steps (our algorithm runs in O(n3+t ) for the undirected version of the bottleneck traveling salesman problem). We also discuss polynomial heuristic algorithms for the bottleneck k-clique problem and the bottleneck k-Iocation problem. We prove using our probabilistic analysis that these algorithms with high probability (whp) produce the optimal solution. Furthermore, we extend our results to the d·th best solution for some bottleneck optimization problems. -This research was supported by AFOSR Grant 90-0107, and in part by the NSF Grant CCR.890030S, and by Grant ROI LM05118 from the Na.tional Library of Medicine.