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A Nearly Optimal Deterministic Algorithm for Online Transportation Problem

Authors Tsubasa Harada , Toshiya Itoh

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ACM Subject Classification
  • Theory of computation → Online algorithms
Keywords
  • Online algorithms
  • Competitive analysis
  • Online metric matching
  • Online weighted matching
  • Online minimum weight perfect matching
  • Online transportation problem
  • Online facility assignment
  • Greedy algorithm

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Abstract

For the online transportation problem with m server sites, it has long been known that the competitive ratio of any deterministic algorithm is at least 2m-1. Kalyanasundaram and Pruhs conjectured in 1998 that a deterministic (2m-1)-competitive algorithm exists for this problem, a conjecture that has remained open for over two decades.
In this paper, we propose a new deterministic algorithm for the online transportation problem and show that it achieves a competitive ratio of at most 8m-5. This is the first O(m)-competitive deterministic algorithm, coming close to the lower bound of 2m-1 within a constant factor.

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Tsubasa Harada and Toshiya Itoh. A Nearly Optimal Deterministic Algorithm for Online Transportation Problem. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 94:1-94:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.94

Author Details

Tsubasa Harada
  • Institute of Science Tokyo, Japan
Toshiya Itoh
  • Institute of Science Tokyo, Japan

Funding

This work was partially supported by Japan Science and Technology Agency (JST) as part of Adopting Sustainable Partnerships for Innovative Research Ecosystem (ASPIRE), Grant Number JPMJAP2302.

References

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