An Optimal Algorithm for Generating Equivalence Relations on a Linear Array of Processors

we describe a cost-optimal parallel algorithm for enumerating all partitions (equivalence relations) of the set {l' ' ' ' 'n},in lexicographic order. The algorithm is designed io be executed on a linear array of processors' It uses n processors' each having ionstant size memory and each being responsrble for producing one element ofa given set partition. set partitions are generated with constant delay leading to an o(8,) time solution, where B, is the total numbei of set partitions. The same method can be generalized Io enumerate some other combinatorial objects such as viriations. The algorithm can be made adaptive, i e' to run on any prespecified number oflrocessors. To illustrate ttre rn'oaet "ipur"il"r computation, a s i m p l e c a s e o f e n u m e r a t i n g s u b s e t s o f t h e s e t u , . . . , r l h a v i n g a t o r , , t < r t e l e m e n t s i s a l s o described. C R categories: C. l, F.2.