K-Dimensional Optimal Parallel Algorithm for the solution of a general class of recurrence equations

This paper proposes a parallel algorithm, called KDOP (K-Dimensional Optimal Parallel algorithm), to solve a general class of recurrence equations efficiently. The KDOP algorithm partitions the computation into a series of subcomputations, each of which is executed in the fashion that all the processors work simultaneously with each one executing an optimal sequential algorithm to solve a subcomputation task. The algorithm solves the equations inO(N/p) steps in EREW PRAM model (Exculsive Read Exclusive Write Parallel Random Access Machine model) usingp≤N1-∈ processors, whereN is the size of the problem, and ∈ is a given constant. This is an optimal algorithm (its speedup isO(p)) in the case ofp≤N1-∈. Such an optimal speedup for this problem was previously achieved only in the case ofp≤N0.5. The algorithm can be implemented on machines with multiple processing elements or pipelined vector machines with parallel memory systems.

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