MPI-I-97-1-021

Novel algorithms are presented for parallel and external memory list-ranking. The same algorithms can be used for computing basic tree functions, such as the depth of a node. The parallel algorithm stands out through its low memory use, its simplicity and its performance. For a large range of problem sizes, it is almost as fast as the fastest previous algorithms. On a Paragon with 100 PUs, each holding 10^6 nodes, we obtain speed-up 25. For external-memory list-ranking, the best algorithm so far is an optimized version of independent-set-removal. Actually, this algorithm is not good at all: for a list of length N, the paging volume is about 72 N. Our new algorithm reduces this to 18 N. The algorithm has been implemented, and the theoretical results are confirmed.