One-by-One Cleaning for Practical Parallel List Ranking

Abstract

It is hard to achieve good speed-ups for parallel list ranking on distributed-memory machines because the problem requires a substantial number of communication rounds, each incurring some start-up delay. For input sizes Nthat are very large in comparison with the number of processors Pthese start-up costs can be amortized to a certain extent. For modest N/Pvalues, so far the best approach was the basic pointer-jumping approach. In this paper a novel algorithm, one-by-one cleaning , is presented. It has the unique property that the routing consists of O(P)rounds in which each processing unit (PU) sends a packet to only one other PU. Pointer jumping requires a logarithmic number of rounds in which each PU sends a packet to all other PUs. Because the constants are small, and the internal work performed is less than that of pointer jumping, one-by-one cleaning is about twice as fast, which is demonstrated by comparing the performance of implementations of both algorithms on the Intel Paragon.