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<p>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/sup 1+ epsilon /) for any constant epsilon, and in time O(n log n/p+log/sup 3/ p) otherwise. This clearly attains a linear speedup when n= Omega (p/sup 1+ epsilon /). 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.</p>
Index Termsload balancing; graph algorithms; sorting; list ranking; graph problems; hypercube algorithm; linear speedup; hypercube algorithms; basic graph problems; tree expression evaluation; biconnected components; ear decomposition; st-numbering; one-port communication; computational complexity; graph theory; parallel algorithms; sorting

J. JáJ? and K. Ryu, "Efficient Algorithms for List Ranking and for Solving Graph Problems on the Hypercube," in IEEE Transactions on Parallel & Distributed Systems, vol. 1, no. , pp. 83-90, 1990.
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