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

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 M (multi-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 M outperforms the classic algorithm in all cases. The algorithm S (start-up cost) that is developed herein includes the computation and communication start-up costs. Finally, two algorithms M and S are combined to form algorithm MS with even better performance than each.