Parallel Recursive Computations where Both Recombination and Partition Overheads are Problem-Dependent

Abstract

Parallel recursive computations incorporating the unavoidable and significant parallel computing overheads, encompassing a wide variety of applications, can be modeled as T(n) = left{ {mathop {min }limits_{0 le r le n}^{t_{(),} } } right.left{ {max left{ {T(n - r),T(r) + k(r)} right} + mathop {mathop {lambda (n,r)}limits_{otherwise} }limits^{forn le n_{(),} } } right} where k(r) and X(n,r) represent the partition and recombination overheads respectively. The optimal partition size (solution to r of the above minmax recurrence relation) is nontrivial and is very different from the n/2 value conventionally used. Using the optimal partitions at every stage of the recursion enhances the performance greatly. In this paper we solve a challenging case of our parallel recursive model where the overhead functions are problem-dependent.