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A family of computationefficient parallel prefix algorithms
 WSEAS Trans. Comput
, 2006
"... Abstract: We are interested in solving the prefix problem of n inputs using p < n processors on completely connected distributedmemory multicomputers (CCDMMs). This paper improves a previous work in three respects. First, the communication time of the previous algorithm is reduced significantly ..."
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Abstract: We are interested in solving the prefix problem of n inputs using p < n processors on completely connected distributedmemory multicomputers (CCDMMs). This paper improves a previous work in three respects. First, the communication time of the previous algorithm is reduced significantly. Second, we show that p(p + 1)/2 < n is required for the new algorithm and the original one to be applicable. Third, we argue that for the new algorithm to be faster than other algorithms run on CCDMMs, n> p3 is required. The new algorithm can achieve linear speedup and is costoptimal when n = Ω(p2 log p).
Four Families of ComputationEfficient Parallel Prefix Algorithms for Multicomputers
, 2008
"... Four families of computationefficient parallel prefix algorithms for messagepassing multicomputers are presented. The first two families generalize previous algorithms that use only halfduplex communications, and thus can improve the running time. The third and fourth families adopt collective co ..."
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Four families of computationefficient parallel prefix algorithms for messagepassing multicomputers are presented. The first two families generalize previous algorithms that use only halfduplex communications, and thus can improve the running time. The third and fourth families adopt collective communication operations to reduce the communication times of the first two, respectively. The precondition of all the presented algorithms is also derived. These families each provide the flexibility of choosing either less computation time or less communication time to achieve the minimal running time depending on the ratio of the time required by a communication step to the time required by a computation step. Keywords: Computationefficient; Cost optimality; Messagepassing multicomputers; Parallel algorithms; Prefix computation
Waistsize optimal parallel prefix circuits
, 2007
"... A class of parallel algorithms solving the prefix problem on the circuit model are presented. These prefix circuits are problemsize independent, and can be faster than other prefix circuits when the problem size is greater than the circuit width. The prefix circuits are compared analytically with o ..."
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A class of parallel algorithms solving the prefix problem on the circuit model are presented. These prefix circuits are problemsize independent, and can be faster than other prefix circuits when the problem size is greater than the circuit width. The prefix circuits are compared analytically with other prefix circuits to show how fast they are. Keywords: Combinational circuit; Parallel algorithms; Prefix operation; Problemsize independent; Waistsize optimal. 1.