Efficient algorithms for list ranking and for solving graph problems on the hypercube

TitleEfficient algorithms for list ranking and for solving graph problems on the hypercube
Publication TypeJournal Articles
Year of Publication1990
AuthorsRyu KW, JaJa JF
JournalParallel and Distributed Systems, IEEE Transactions on
Pagination83 - 90
Date Published1990/01//
ISBN Number1045-9219
Keywordsalgorithm;hypercube, algorithms;graph, algorithms;linear, algorithms;sorting;, balancing;one-port, basic, communication;sorting;st-numbering;tree, complexity;graph, components;ear, decomposition;graph, evaluation;computational, Expression, graph, problems;biconnected, problems;hypercube, ranking;load, speedup;list, theory;parallel

A hypercube algorithm to solve the list ranking problem is presented. Let n be the length of the list, and let p be the number of processors of the hypercube. The algorithm described runs in time O(n/p) when n= Omega;(p 1+ epsi;) for any constant epsi; gt;0, and in time O(n log n/p+log3 p) otherwise. This clearly attains a linear speedup when n= Omega;(p 1+ epsi;). Efficient balancing and routing schemes had to be used to achieve the linear speedup. The authors use these techniques to obtain efficient hypercube algorithms for many basic graph problems such as tree expression evaluation, connected and biconnected components, ear decomposition, and st-numbering. These problems are also addressed in the restricted model of one-port communication