Processor-Efficient Hypercube Algorithms for the Knapsack Problem

Abstract A processor-efficient parallel algorithm is presented for the 0/1 knapsack problem. The algorithm can run on any number of processors specified by a user and, more importantly, it has optimal time speedup and processor efficiency over the best known sequential algorithm. Most of the existing parallel algorithms for the problem have high processor complexity and low processor efficiency. These algorithms are useful when the problem size is relatively small. One parallel algorithm has been proposed to run on fewer processors but it has much higher time complexity. The parallel algorithm proposed here is more efficient and practical even for large problem sizes. Experimental results on the Connection Machine show that the algorithm performs very well for a wide range of input sizes.

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