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Traveling Repairperson, Unrelated Machines, and Other Stories About Average Completion Times

Authors Marcin Bienkowski , Artur Kraska , Hsiang-Hsuan Liu

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Author Details

Marcin Bienkowski
  • Institute of Computer Science, University of Wrocław, Poland
Artur Kraska
  • Institute of Computer Science, University of Wrocław, Poland
Hsiang-Hsuan Liu
  • Utrecht University, The Netherlands

Funding

Supported by Polish National Science Centre grant 2016/22/E/ST6/00499.

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Marcin Bienkowski, Artur Kraska, and Hsiang-Hsuan Liu. Traveling Repairperson, Unrelated Machines, and Other Stories About Average Completion Times. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ICALP.2021.28

Abstract

We present a unified framework for minimizing average completion time for many seemingly disparate online scheduling problems, such as the traveling repairperson problems (TRP), dial-a-ride problems (DARP), and scheduling on unrelated machines. 
We construct a simple algorithm that handles all these scheduling problems, by computing and later executing auxiliary schedules, each optimizing a certain function on already seen prefix of the input. The optimized function resembles a prize-collecting variant of the original scheduling problem. By a careful analysis of the interplay between these auxiliary schedules, and later employing the resulting inequalities in a factor-revealing linear program, we obtain improved bounds on the competitive ratio for all these scheduling problems. 
In particular, our techniques yield a 4-competitive deterministic algorithm for all previously studied variants of online TRP and DARP, and a 3-competitive one for the scheduling on unrelated machines (also with precedence constraints). This improves over currently best ratios for these problems that are 5.14 and 4, respectively. We also show how to use randomization to further reduce the competitive ratios to 1+2/ln 3 < 2.821 and 1+1/ln 2 < 2.443, respectively. The randomized bounds also substantially improve the current state of the art. Our upper bound for DARP contradicts the lower bound of 3 given by Fink et al. (Inf. Process. Lett. 2009); we pinpoint a flaw in their proof.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Theory of computation → Scheduling algorithms
Keywords
  • traveling repairperson problem
  • dial-a-ride
  • machine scheduling
  • unrelated machines
  • minimizing completion time
  • competitive analysis
  • factor-revealing LP

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