TY - JOUR T1 - Efficient algorithms for list ranking and for solving graph problems on the hypercube JF - Parallel and Distributed Systems, IEEE Transactions on Y1 - 1990 A1 - Ryu,K. W. A1 - JaJa, Joseph F. KW - algorithm;hypercube KW - algorithms;graph KW - algorithms;linear KW - algorithms;sorting; KW - balancing;one-port KW - basic KW - communication;sorting;st-numbering;tree KW - complexity;graph KW - components;ear KW - decomposition;graph KW - evaluation;computational KW - Expression KW - graph KW - problems;biconnected KW - problems;hypercube KW - ranking;load KW - speedup;list KW - theory;parallel AB - 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 VL - 1 SN - 1045-9219 CP - 1 M3 - 10.1109/71.80127 ER -