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 wellstudied "cowpath 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.
BibTeX  Entry
@InProceedings{coleman_et_al:LIPIcs.OPODIS.2022.12,
author = {Coleman, Jared and Kranakis, Evangelos and Krizanc, Danny and MoralesPonce, Oscar},
title = {{Line Search for an Oblivious Moving Target}},
booktitle = {26th International Conference on Principles of Distributed Systems (OPODIS 2022)},
pages = {12:112:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959772655},
ISSN = {18688969},
year = {2023},
volume = {253},
editor = {Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne},
publisher = {Schloss Dagstuhl  LeibnizZentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/17632},
URN = {urn:nbn:de:0030drops176325},
doi = {10.4230/LIPIcs.OPODIS.2022.12},
annote = {Keywords: Infinite Line, Knowledge, Oblivious, Robot, Search, SearchTime, Speed, Target}
}
Keywords: 

Infinite Line, Knowledge, Oblivious, Robot, Search, SearchTime, Speed, Target 
Collection: 

26th International Conference on Principles of Distributed Systems (OPODIS 2022) 
Issue Date: 

2023 
Date of publication: 

15.02.2023 