Pointers versus Arithmetic in PRAMs

Manipulation of pointers in shared data structures is an important communication mechanism used in many parallel algorithms. Indeed, many fundamental algorithms do essentially nothing else. A Parallel Pointer Machine, (or PPM ) is a parallel model having pointers as its principal data type. PPMs have been characterized as PRAMs obeying two restrictions | rst, restricted arithmetic capabilities, and second, the CROW memory access restriction (Concurrent Read, Owner Write, a commonly occurring special case of CREW). We present results concerning the relative power of PPMs (and other arithmetically restricted PRAMs) versus CROW PRAMs having ordinary arithmetic capabilities. First, we prove lower bounds separating PPMs from CROW PRAMs. For example, any step-by-step simulation of an n-processor CROW PRAM by a PPM requires time (log logn) per step. Second, we show that this lower bound is tight | we give such a step-by-step simulation using O(log logn) time per step. As a corollary, we obtain sharply improved PPM algorithms for a variety of problems, including deterministic context-free language recognition. Research supported by NSERC, the Information Technology Research Centre of Ontario, NSF Grant CCR9002891 and NSF/DARPA Grant CCR-8907960. A portion of this work was performed while the rst and last authors were visiting the University of Toronto, whose hospitality is gratefully acknowledged.