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A Mildly Exponential Time Algorithm for Approximating the Number of Solutions to a Multidimensional Knapsack Problem

We describe a time randomized algorithm that estimates the number of feasible solutions of a multidimensional knapsack problem within 1 ± ε of the exact number. (Here r is the number of constraints and n is the number of integer variables.) The algorithm uses a Markov chain to generate an almost uniform random solution to the problem.