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Improved Bounds for Online TSP on the Half-Line

Authors Júlia Baligács , Yann Disser , Linda Thelen

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LIPIcs.SWAT.2026.4.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
Keywords
  • online algorithms
  • competitive analysis
  • server problems
  • online TSP

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Abstract

In the open online traveling salesperson problem, requests appear over time at different positions of a metric space. A single agent traveling at unit speed must serve all requests, by visiting their positions, with the objective of minimizing the completion time. We propose online algorithms for this problem for the case that the metric space is the half-line. First, we present a 2-competitive algorithm in which the server always either moves at unit speed or remains stationary, which improves on the previously best-known ratio of 2.04. We further observe that algorithms must sometimes move slower than unit speed to achieve competitive ratios below 2. We introduce a second algorithm that beats the barrier of 2 by carefully modulating its speed, and prove a tight bound of 1.75 on its competitive ratio. Finally, we slightly strengthen a known lower bound on the best-possible competitive ratio on the half-line from 1.627 to 1.646.

Cite As Get BibTex

Júlia Baligács, Yann Disser, and Linda Thelen. Improved Bounds for Online TSP on the Half-Line. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SWAT.2026.4

Author Details

Júlia Baligács
  • University of Warsaw, Poland
Yann Disser
  • TU Darmstadt, Germany
Linda Thelen
  • TU Darmstadt, Germany

Funding

  • Baligács, Júlia: Supported by the project BOBR that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 948057).

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