Lower bounds for recognizing small cliques on CRCW PRAM's

Abstract

We show that any CRCW PRAM which recognizes k-cliques in n-node graphs in time T requires at least n Ω( K T 2) processors independent of its memory size. As a corollary we obtain essentially the same trade-off for unbounded fan-in circuits. We also demonstrate a similar but weaker trade-off for the memory size of CRCW PRAM's solving this problem independent of the number of processors. These bounds also answer an open question posed in [13], i.e., they show that constant-depth circuits for recognizing k-cliques in n-node graphs require size n ⊖(k) .