A sparse knapsack algo-tech-cuit and its synthesis

We systematically derive an improved algorithm (called the sparse algorithm) for the general knapsack problem which has better average case performance than the standard (dense) dynamic programming algorithm. The derivation is based on transformation of the standard recurrences into stream functional programs, and cannot be achieved by the usual space-time mapping techniques because the dependencies are statically unpredictable. Furthermore such a sparse algorithm for the general knapsack problem has not been proposed in the literature, to the best of our knowledge. We also implement the sparse algorithm on a linear asynchronous array with constant size memory on each PE (i.e., a wavefront array processor). Using LPGS partitioning, the algorithm can run on an arbitrary size ring and has optimal time speedup