Scheduling with Communication Delays via LP Hierarchies and Clustering

Sami Davies; Janardhan Kulkarni; Thomas Rothvoss; Jakub Tarnawski; Yihao Zhang

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arXiv · 2004.09682

Scheduling with Communication Delays via LP Hierarchies and Clustering

Sami Davies·Janardhan Kulkarni·Thomas Rothvoss·Jakub Tarnawski·Yihao Zhang

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Abstract

We consider the classic problem of scheduling jobs with precedence constraints on identical machines to minimize makespan, in the presence of communication delays. In this setting, denoted by $\mathsf{P} \mid \mathsf{prec}, c \mid C_{\mathsf{max}}$, if two dependent jobs are scheduled on different machines, then at least $c$ units of time must pass between their executions. Despite its relevance to many applications, this model remains one of the most poorly understood in scheduling theory. Even for a special case where an unlimited number of machines is available, the best known approximation ratio is $2/3 \cdot (c+1)$, whereas Graham's greedy list scheduling algorithm already gives a $(c+1)$-approximation in that setting. An outstanding open problem in the top-10 list by Schuurman and Woeginger and its recent update by Bansal asks whether there exists a constant-factor approximation algorithm. In this work we give a polynomial-time $O(\log c \cdot \log m)$-approximation algorithm for this problem, where $m$ is the number of machines and $c$ is the communication delay. Our approach is based on a Sherali-Adams lift of a linear programming relaxation and a randomized clustering of the semimetric space induced by this lift.

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BibTeX RIS

Sami Davies, Janardhan Kulkarni, Thomas Rothvoss, Jakub Tarnawski, Yihao Zhang. 2020-04-21. Scheduling with Communication Delays via LP Hierarchies and Clustering. https://arxiv.org/abs/2004.09682

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