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Scheduling with Communication Delay in Near-Linear Time

Authors Quanquan C. Liu, Manish Purohit, Zoya Svitkina, Erik Vee, Joshua R. Wang

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Author Details

Quanquan C. Liu
  • MIT, CSAIL, Cambridge, MA, US
Manish Purohit
  • Google Research, Mountain View, CA, USA
Zoya Svitkina
  • Google Research, Mountain View, CA, USA
Erik Vee
  • Google Research, Mountain View, CA, uSA
Joshua R. Wang
  • Google Research, Mountain View, CA, USA

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Quanquan C. Liu, Manish Purohit, Zoya Svitkina, Erik Vee, and Joshua R. Wang. Scheduling with Communication Delay in Near-Linear Time. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 47:1-47:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.STACS.2022.47

Abstract

We consider the problem of efficiently scheduling jobs with precedence constraints on a set of identical machines in the presence of a uniform communication delay. Such precedence-constrained jobs can be modeled as a directed acyclic graph, G = (V, E). In this setting, if two precedence-constrained jobs u and v, with v dependent on u (u ≺ v), are scheduled on different machines, then v must start at least ρ time units after u completes. The scheduling objective is to minimize makespan, i.e. the total time from when the first job starts to when the last job finishes. The focus of this paper is to provide an efficient approximation algorithm with near-linear running time. We build on the algorithm of Lepere and Rapine [STACS 2002] for this problem to give an O((ln ρ)/(ln ln ρ))-approximation algorithm that runs in Õ(|V|+|E|) time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Scheduling algorithms
Keywords
  • near-linear time scheduling
  • scheduling with duplication
  • precedence-constrained jobs
  • graph algorithms

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