A Parallel O(n2~(7n/8)) Time-Memory-Processor Tradeoff for Knapsack-Like Problems

摘要

A general-purpose parallel three-list four-table algorithm that can solve a number of knapsack-like NP-complete problems is developed in this paper. Running on an EREW PRAM model, The proposed parallel algorithm can solve this kind of problems of size n in O(n2~(9n/20)) time, with O(2~(13n/40)) shared memory units and O(2~(n/10)) processors, and thus its time-space-processor tradeoff is O(n2~(7n/8)). The performance analysis and comparisons show that the proposed algorithms are both time and space efficient, and thus is an improved result over the past researches. Since it can break greater variables knapsack-based cryptosystems and watermark, the new algorithm has some cryptanalytic significance.