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Lower Bounds for Shoreline Searching With 2 or More Robots

Authors Sumi Acharjee, Konstantinos Georgiou, Somnath Kundu, Akshaya Srinivasan

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Author Details

Sumi Acharjee
  • Department of Mathematics, Ryerson University, Toronto, Canada
Konstantinos Georgiou
  • Department of Mathematics, Ryerson University, Toronto, Canada
Somnath Kundu
  • Department of Mathematics, Ryerson University, Toronto, Canada
Akshaya Srinivasan
  • Department of Computer Science & Engineering, National Institute of Technology, Tiruchirappalli, India

Funding

  • Georgiou, Konstantinos: Research supported in part by NSERC.
  • Srinivasan, Akshaya: Research supported in part by MITACS Globalink.

Cite As Get BibTex

Sumi Acharjee, Konstantinos Georgiou, Somnath Kundu, and Akshaya Srinivasan. Lower Bounds for Shoreline Searching With 2 or More Robots. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 26:1-26:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.OPODIS.2019.26

Abstract

Searching for a line on the plane with n unit speed robots is a classic online problem that dates back to the 50’s, and for which competitive ratio upper bounds are known for every n ≥ 1, see [Baeza-Yates and Schott, 1995]. In this work we improve the best lower bound known for n=2 robots [Baeza-Yates and Schott, 1995] from 1.5993 to 3. Moreover we prove that the competitive ratio is at least √{3} for n=3 robots, and at least 1/cos ({π/n}) for n ≥ 4 robots. Our lower bounds match the best upper bounds known for n ≥ 4, hence resolving these cases. To the best of our knowledge, these are the first lower bounds proven for the cases n ≥ 3 of this several decades old problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Theory of computation → Distributed algorithms
  • Theory of computation → Computational geometry
  • Computing methodologies → Continuous space search
Keywords
  • 2-Dimensional Search
  • Online Algorithms
  • Competitive Analysis
  • Lower Bounds

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