eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-02-15
12:1
12:19
10.4230/LIPIcs.OPODIS.2022.12
article
Line Search for an Oblivious Moving Target
Coleman, Jared
1
https://orcid.org/0000-0003-1227-2962
Kranakis, Evangelos
2
https://orcid.org/0000-0002-8959-4428
Krizanc, Danny
3
Morales-Ponce, Oscar
4
https://orcid.org/0000-0002-9645-1257
University of Southern California, Los Angeles, CA, USA
Carleton University, Ottawa, Canada
Wesleyan University, Middletown, CT, USA
California State University, Long Beach, CA, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol253-opodis2022/LIPIcs.OPODIS.2022.12/LIPIcs.OPODIS.2022.12.pdf
Infinite Line
Knowledge
Oblivious
Robot
Search
Search-Time
Speed
Target