Negative Instance for the Edge Patrolling Beacon Problem
Computational Geometry
2020-06-03 v1
Abstract
Can an infinite-strength magnetic beacon always ``catch'' an iron ball, when the beacon is a point required to be remain nonstrictly outside a polygon, and the ball is a point always moving instantaneously and maximally toward the beacon subject to staying nonstrictly within the same polygon? Kouhestani and Rappaport [JCDCG 2017] gave an algorithm for determining whether a ball-capturing beacon strategy exists, while conjecturing that such a strategy always exists. We disprove this conjecture by constructing orthogonal and general-position polygons in which the ball and the beacon can never be united.
Cite
@article{arxiv.2006.01202,
title = {Negative Instance for the Edge Patrolling Beacon Problem},
author = {Zachary Abel and Hugo A. Akitaya and Erik D. Demaine and Martin L. Demaine and Adam Hesterberg and Matias Korman and Jason S. Ku and Jayson Lynch},
journal= {arXiv preprint arXiv:2006.01202},
year = {2020}
}
Comments
Full version of a JCDCGGG2018 paper, 8 pages, 4 figures