Parallel algorithms for relational coarsest partition problems
Sundaramoorthy Rajasekaran, I. Lee · IEEE Transactions on Parallel and Distributed Systems · 1998
Relational Coarsest Partition Problems (RCPPs) play a vital role in verifying concurrent systems. It is known that RCPPs are P-complete and hence it may not be possible to design polylog time parallel algorithms for these problems. In this paper, we present two efficient parallel algorithms for RCPP in which its associated label transition system is assumed to have m transitions and n states. The first algorithm runs in O(n/sup 1+/spl epsiv//) time using m/n/sup /spl epsiv// CREW PRAM processors, for any fixed /spl epsiv/<1. This algorithm is analogous to and optimal with respect to the sequential algorithm of P.C. Kanellakis and S.A. Smolka (1990). The second algorithm runs in O(n log n) time using m/n CREW PRAM processors. This algorithm is analogous to and nearly optimal with respect to the sequential algorithm of R. Paige and R.E. Tarjan (1987).