A Guaranteed Approximation Algorithm for Scheduling Fork-Joins with Communication Delay

Abstract

Scheduling task graphs with communication delay is a widely studied NP-hard problem. Many heuristics have been proposed, but there is no constant approximation algorithm for this classic model. In this paper, we focus on the scheduling of the important class of fork-join task graphs (describing many types of common computations) on homogeneous processors. For this sub-case, we propose a guaranteed algorithm with a $\left( {1 + \frac{m}{{m - 1}}} \right)$-approximation factor, where m is the number of processors. The algorithm is not only the first constant approximation for an important sub-domain of the classic scheduling problem, it is also a practical algorithm that can obtain shorter makespans than known heuristics. To demonstrate this, we propose adaptations of known scheduling heuristic for the specific fork-join structure. In an extensive evaluation, we then implemented these algorithms and scheduled many fork-join graphs with up to thousands of tasks and various computation time distributions on up to hundreds of processors. Comparing the obtained results demonstrates the competitive nature of the proposed approximation algorithm.