We consider problems on networks that are captured by two performance measures. One performance measure is any general cost function of a solution; the other is a bottleneck measure that describes the worst (maximum cost) component of the solution. The paper contains algorithms to solve three problems. In one problem, we minimize the bottleneck subject to a constraint on the generalized cost. In the second problem, we minimize the generalized cost subject to a constraint on the bottleneck. In the third problem, we consider the two criteria simultaneously and find all the Pareto optimum solutions. The major result is that the introduction of the bottleneck measure changes the complexity of the original (general cost) problem by a factor which is at most linear in the number of links.
This paper focuses on managing the cost of de liberation before action. In many problems, the cost and the resource consumption of the delib eration phase cannot be ignored, and the overall quality of the solution refl ects the costs incurred and the resources consumed in deliberation as well as the cost and benefit of execution. A feasible strategy that minimizes the total cost is termed computationally-optimal. For a situation where a number of independent, uninterruptible meth ods are available to solve the problem, we develop a pseudopolynomial-time algorithm to construct generate-and-test computationally-optimal strate gies. Stochastic Dynamic Programming is used to solve the problem that is shown to be NP-complete and the results address problems occurring in auto matic emergency-response systems, design automa tion, query optimization, destructive testing, and other areas characterized by significant computa tional costs or limited deliberation resources.
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