WECPAR: List Ranking Algorithm and Relative Computational Power

Abstract

Reconfigurable models were shown to be very powerful in solving many problems faster than non reconfigurable models. WECPAR W(M,N,k) is an M × N reconfigurable model that has point-to-point reconfigurable interconnection with k wires between neighboring processors. This paper studies several aspects of WECPAR. We first solve the list ranking problem on WECPAR. Some of the results obtained show that ranking one element in a list of N elements can be solved on W(N,N,N) WECPAR in O(1) time. Also, on W(N,N,k), ranking a list L(N) of N elements can be done in O((log N)([logk+1])) time. To transfer a large body of algorithms to work on WECPAR and to assess its relative computational power, several simulations algorithms are introduced between WECPAR and well-known models such as PRAM and RMBM. Simulations algorithms show that a PRIORITY CRCW PRAM of N processors and S shared memory locations can be simulated by an W(S, N, k) WECPAR in O([logk+1 N]+[log Sk+1]) time. Also, we show that a PRIORITY CRCW Basic-RMBM(P,B), of P processors and B buses can be simulated by an W(B, P+B, k) WECPAR in O([logk+1 (P+B)]) time. This has the effect of migrating a large number of algorithms to work directly on WECPAR with the simulation overhead.