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[LSS88] In the parallel formulation of the 0/1 knapsack problem presented in Section 12.2.2, the degree of concurrency is proportional to c, the knapsack capacity. Also this algorithm has limited data locality, as the amount of data to be communicated is of the same order of magnitude as the computation at each processing element. Lee et al. present another formulation in which the degree of concurrency is proportional to n, the number of weights. This formulation also has much more data locality. In this formulation, the set of weights is partitioned among processing elements. Each processing element computes the maximum profit it can achieve from its local weights for knapsacks of various sizes up to c. This information is expressed as lists that are merged to yield the global solution. Compute the parallel run time, speedup, and efficiency of this formulation. Compare the performance of this algorithm with that in Section 12.2.2.
Understand the concepts relating to issues
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