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A Deterministic Fully Polynomial Time Approximation Scheme For Counting Integer Knapsack Solutions Made Easy Halman, Nir Approximate counting integer knapsack dynamic programming bounding constraints $K$-approximating sets and functions Given n elements with nonnegative integer weights w=(w_1,...,w_n), an integer capacity C and positive integer ranges u=(u_1,...,u_n), we consider the counting version of the classic integer knapsack problem: find the number of distinct multisets whose weights add up to at most C. We give a deterministic algorithm that estimates the number of solutions to within relative error epsilon in time polynomial in n, log U and 1/epsilon, where U=max_i u_i. More precisely, our algorithm runs in O((n^3 log^2 U)/epsilon) log (n log U)/epsilon) time. This is an improvement of n^2 and 1/epsilon (up to log terms) over the best known deterministic algorithm by Gopalan et al. [FOCS, (2011), pp. 817-826]. Our algorithm is relatively simple, and its analysis is rather elementary. Our results are achieved by means of a careful formulation of the problem as a dynamic program, using the notion of binding constraints. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Nir Halman 2016 Is Part Of LIPIcs, Volume 60, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX-RANDOM.2016.9 urn:nbn:de:0030-drops-66327 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2016.9 eng https://creativecommons.org/licenses/by/3.0/legalcode