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Line Search for an Oblivious Moving Target

Authors Jared Coleman , Evangelos Kranakis , Danny Krizanc, Oscar Morales-Ponce



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Author Details

Jared Coleman
  • University of Southern California, Los Angeles, CA, USA
Evangelos Kranakis
  • Carleton University, Ottawa, Canada
Danny Krizanc
  • Wesleyan University, Middletown, CT, USA
Oscar Morales-Ponce
  • California State University, Long Beach, CA, USA

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Jared Coleman, Evangelos Kranakis, Danny Krizanc, and Oscar Morales-Ponce. Line Search for an Oblivious Moving Target. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 253, pp. 12:1-12:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.OPODIS.2022.12

Abstract

Consider search on an infinite line involving an autonomous robot starting at the origin of the line and an oblivious moving target at initial distance d ≥ 1 from it. The robot can change direction and move anywhere on the line with constant maximum speed 1 while the target is also moving on the line with constant speed v > 0 but is unable to change its speed or direction. The goal is for the robot to catch up to the target in as little time as possible. The classic case where v = 0 and the target’s initial distance d is unknown to the robot is the well-studied "cow-path problem". Alpert and Gal [Steve Alpern and Shmuel Gal, 2003] gave an optimal algorithm for the case where a target with unknown initial distance d is moving away from the robot with a known speed v < 1. In this paper we design and analyze search algorithms for the remaining possible knowledge situations, namely, when d and v are known, when v is known but d is unknown, when d is known but v is unknown, and when both v and d are unknown. Furthermore, for each of these knowledge models we consider separately the case where the target is moving away from the origin and the case where it is moving toward the origin. We design algorithms and analyze competitive ratios for all eight cases above. The resulting competitive ratios are shown to be optimal when the target is moving towards the origin as well as when v is known and the target is moving away from the origin.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Theory of computation → Adversary models
Keywords
  • Infinite Line
  • Knowledge
  • Oblivious
  • Robot
  • Search
  • Search-Time
  • Speed
  • Target

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