Scheduling UET-UCT DAGs of Depth Two on Two Processors

TL;DR

This paper presents a linear time algorithm for optimally scheduling depth-two DAGs with unit execution and communication times on two processors, addressing a complex open problem in task scheduling.

Contribution

It introduces a novel linear time algorithm that computes optimal schedules for depth-two DAGs, expanding the class of efficiently solvable scheduling problems.

Findings

The algorithm computes optimal schedules in linear time.

It solves the scheduling problem for depth-two DAGs exactly.

The approach improves understanding of scheduling complexity for specific DAG classes.

Abstract

Given unit execution time (UET) tasks whose precedence constraints form a directed acyclic graph (DAG), the arcs are associated with unit communication time (UCT) delays. The problem is to schedule the tasks on two processors in order to minimize the makespan. Several polynomial algorithms in the literature are proposed for special classes of digraphs, but the complexity of solving this problem in general case stills a challenging open question. We propose in this paper a linear time algorithm to compute an optimal schedule for the class of DAGs of depth two.