We describe a 2 O(r √ n(log n) 5/2 ) ǫ −2 time randomized algorithm which estimates the number of feasible solutions of a multidimensional knapsack problem within 1 ± ǫ of the exact number. (Here r is the number of constraints and n is the number of integer variables.) The algorithm 1 uses a Markov chain to generate an almost uniform random solution to the problem.
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