An O(n) algorithm for the linear multiple choice knapsack problem and related problems
Information Processing Letters
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Knapsack problems: algorithms and computer implementations
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IEEE Transactions on Image Processing
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DEXA'05 Proceedings of the 16th international conference on Database and Expert Systems Applications
Optimizing adaptive multi-route query processing via time-partitioned indices
Journal of Computer and System Sciences
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We show that the problem of optimal bit allocation among a set of independent discrete quantizers given a budget constraint is equivalent to the multiple choice knapsack problem (MCKP). This result has three implications: first, it provides a trivial proof that the problem of optimal bit allocation is NP-hard and that its related decision problem is NP-complete; second, it unifies research into solving these problems that has to-date been done independently in the data compression community and the operations research community; third, many practical algorithms for approximating the optimal solution to MCKP can be used for bit allocation. We implement the GBFOS, Partition-Search, and Dudzinski-Walukiewicz algorithms and compare their running times for a variety of problem sizes.