Abstract
The recurrencex o =a o x i =a i+b i x i−1,i = 1, 2,...,n−1 requiresO(n) operations on a sequential computer. Elegant parallel solutions exist, however, that reduce the complexity toO(logN) usingN⩾n processors. This paper discusses one such solution, designed for a tree-structured network of processors.
A tree structure is ideal for solving recurrences. It takes exactly one sweep up and down the tree to solve any of several classes of recurrences, thus guaranteeing a solution inO(logN) time for a tree withN⩾n leaf nodes. Ifn exceedsN, the algorithm efficiently pipelines the operation and solves the recurrence inO(n/N + logN) time.
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Pargas, R.P. Parallel solution of recurrences on a tree machine. International Journal of Computer and Information Sciences 13, 251–277 (1984). https://doi.org/10.1007/BF00977832
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DOI: https://doi.org/10.1007/BF00977832