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Scheduling with Locality by Routing

Authors Alison Hsiang-Hsuan Liu , Fu-Hong Liu

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Author Details

Alison Hsiang-Hsuan Liu
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
Fu-Hong Liu
  • Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu, Taiwan

Acknowledgements

The authors would like to thank Sheng-Yin Chen and Chung-Shou Liao for their discussions in the early stages.

Cite AsGet BibTex

Alison Hsiang-Hsuan Liu and Fu-Hong Liu. Scheduling with Locality by Routing. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 69:1-69:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.MFCS.2024.69

Abstract

This work examines a strongly NP-hard routing problem on trees, in which multiple servers need to serve a given set of requests (on vertices), where the routes of the servers start from a common source and end at their respective terminals. Each server can travel free of cost on its source-to-terminal path but has to pay for travel on other edges. The objective is to minimize the maximum cost over all servers. As the servers may pay different costs for traveling through a common edge, balancing the loads of the servers can be difficult. We propose a polynomial-time 4-approximation algorithm that applies the parametric pruning framework but consists of two phases. The first phase of the algorithm partitions the requests into packets, and the second phase of the algorithm assigns the packets to the servers. Unlike the standard parametric pruning techniques, the challenge of our algorithm design and analysis is to harmoniously relate the quality of the partition in the first phase, the balances of the servers' loads in the second phase, and the hypothetical optimal values of the framework. For the problem in general graphs, we show that there is no algorithm better than 2-approximate unless P = NP. The problem is a generalization of unrelated machine scheduling and other classic scheduling problems. It also models scheduling problems where the job processing times depend on the machine serving the job and the other jobs served by that machine. This modeling provides a framework that physicalizes scheduling problems through the graph’s point of view.

Subject Classification

ACM Subject Classification
  • Theory of computation → Routing and network design problems
Keywords
  • Makespan minimization
  • Approximation algorithms
  • Routing problems
  • Parametric pruning framework

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