Issue No. 10 - October (1996 vol. 7)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/71.539738
<p><b>Abstract</b>—We consider the problem of scheduling tasks on multiprocessor architectures in the presence of communication delays. Given a set of dependent tasks, the <it>scheduling problem</it> is to allocate the tasks to processors such that the pre-specified precedence constraints among the tasks are obeyed and certain cost-measures (such as the computation time) are minimized. Several cases of the scheduling problem have been proven to be NP-complete [<ref rid="bibl106516" type="bib">16</ref>], [<ref rid="bibl106510" type="bib">10</ref>]. Nevertheless, there are polynomial time algorithms for interesting special cases of the general scheduling problem [<ref rid="bibl106512" type="bib">12</ref>], [<ref rid="bibl106514" type="bib">14</ref>], [<ref rid="bibl106510" type="bib">10</ref>]. Most of these results, however, do not take into consideration the delays due to message passing among processors. In this paper we study the increase in time complexity of scheduling problems due to the introduction of communication delays. In particular, we address the open problem of scheduling Out-forests (In-forests) in a multiprocessor system of <it>m</it> identical processors when communication delays are considered. The corresponding problem of scheduling Out-forests (In-forests) without communication delays admits an elegant polynomial time solution as presented first by Hu in 1961 [<ref rid="bibl106512" type="bib">12</ref>]; however, the problem in the presence of communication delays has remained unsolved. We present here first known polynomial time algorithms for the computation of the optimal schedule when the number of available processors is given and bounded and both computation and communication delays are assumed to take one unit of time. Furthermore, we present a <it>linear-time</it> algorithm for computing a <it>near-optimal</it> schedule for unit-delay out-forests. The schedule's length exceeds the optimum by no more than (<it>m</it>– 2) time units, where <it>m</it> is the number of processors. Hence for two processors the computed schedule is strictly optimum.</p>
Communication delays, out-forest precedence graphs, multiprocessor architectures, out-forest precedence graphs, optimal deterministic schedules, polynomial-time algorithms.
T. A. Varvarigou, T. Kailath, V. P. Roychowdhury and E. Lawler, "Scheduling In and Out Forests in the Presence of Communication Delays," in IEEE Transactions on Parallel & Distributed Systems, vol. 7, no. , pp. 1065-1074, 1996.