A model of sequential computation with Pipelined access to memory

Abstract

We introduce a new sequential model of computation, called the Logarithmic Pipelined Model (LPM), in which a RAM processor of fixed size has pipelined access to a memory ofm cells in time logm. Our motivation is that the usual assumption that a memory can be accessed in constant time becomes theoretically unacceptable asm increases, while an access time of logm is consistent with VLSI technologies. For a problem II of sizen, IT εP, we denote byS(n) the time required by the fastest known sequential algorithm, and byT(n) the time required by the fastest algorithm solving II in the LPM. LettingO(logn) =O(logm), we define several complexity classes; in particular, LP₀ = {II εP:T(n) =O(S(n))}, the class of problems for which the LPM is as efficient as the standard model, and LP_∞ =IIεP:T(n) =O(S(n) logn), where the problems are less adequately solved in the new model. We first study the relations between the LPM and other models of computation. Of particular relevance is comparison with the PRAM model. Then we discuss several problems and derive the relative upper and lower bounds in the LPM. Our results lead to a new organization of parallel algorithms for list-linked structures.