A Faster FPTAS for #Knapsack
Pawe{\l} Gawrychowski, Liran Markin, Oren Weimann

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Abstract
Given a set of non-negative integer weights and an integer , the #Knapsack problem asks to count the number of distinct subsets of whose total weight is at most . In the more general integer version of the problem, the subsets are multisets. That is, we are also given a set and we are allowed to take up to items of weight . We present a deterministic FPTAS for #Knapsack running in time. The previous best deterministic algorithm [FOCS 2011] runs in time (see also [ESA 2014] for a logarithmic factor improvement). The previous best randomized algorithm [STOC 2003] runs in time. Therefore, in the natural setting of constant…
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