Abstract:
We consider the well known problem of determining the k'th vertex reached by chasing pointers in a directed graph of out-degree 1. The famous "pointer doubling" technique provides an O(log k) parallel time algorithm on a Concurrent-Read Exclusive-Write (CREW) PRAM. We prove that this problem requires Omega(k) steps on an Exclusive-Read Exclusive-Write (EREW) PRAM, for every k < (c sqrt(log n)), where n is the number of vertices and c is a constant. This yields a boolean function which can be computed in O(log log n) time on a CREW PRAM, but requires Omega(sqrt (log n)) time on even an `ideal' EREW PRAM. This is the first separation known for boolean functions between the power of EREW and CREW PRAMs. Previously, separations between EREW and CREW PRAMs were only known for functions on `huge' input domains, or for restricted types of EREW PRAMs.