Novel Methods for Divisible Load Distribution with Start-Up Costs on a Complete <italic>b</italic>-Ary Tree

Abstract

This work investigates divisible load distribution using multi-installment processing on complete b -ary tree networks. Classic methods of distributing a divisible load divide the computation and communication processes into multiple time intervals in a pipelined fashion. The algorithm $\mathbb {M}$ ( m ulti-installment) herein uses multi-installment processing with pipelined communication to reduce the initial distribution time and to improve the performance. Closed-form expressions for the parallel processing time and speed-up are derived. This work reveals that the asymptotic speed-up of the proposed algorithm is $b\beta +1$ where $\beta$ is the computation-to-communication ratio of a node in the system. Algorithm $\mathbb {M}$ outperforms the classic algorithm in all cases. The algorithm $\mathbb {S}$ ( s tart-up cost) that is developed herein includes the computation and communication start-up costs. Finally, two algorithms $\mathbb {M}$ and $\mathbb {S}$ are combined to form algorithm $\mathbb {MS}$ with even better performance than each.