Optimal Tree Contraction in the EREW Model
A deterministic parallel algorithm for parallel tree contraction is presented in this paper. The algorithm takes T = O(n/P) time and uses P (P ≤ n/log n) processors, where n = the number of vertices in a tree using an Exclusive Read and Exclusive Write (EREW) Parallel Random Access Machine (PRAM). This algorithm improves the results of Miller and Reif [MR85,MR87], who use the CRCW randomized PRAM model to get the same complexity and processor count. The algorithm is optimal in the sense that the product P · T is equal to the input size and gives an O(log n) time algorithm when P = n/log n. Since the algorithm requires O(n) space, which is the input size, it is optimal in space as well. Techniques for prudent parallel tree contraction are also discussed, as well as implementation techniques for fixed-connection machines.
KeywordsContraction Phase List Ranking Free Vertex Parallel Random Access Machine Compress Operation
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