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On Romeo and Juliet problems: Minimizing distance-to-sight

Title
On Romeo and Juliet problems: Minimizing distance-to-sight
Authors
Ahn, H.-K.Oh, E.Schlipf, L.Stehn, F.Strash, D.
Date Issued
Nov-2019
Publisher
ELSEVIER
Abstract
We introduce a variant of the watchman route problem, which we call the quickest pair-visibility problem. Given two persons standing at points s and t in a simple polygon P with no holes, we want to minimize the distance they travel in order to see each other in P. We solve two variants of this problem, one minimizing the longer distance the two persons travel (min-max) and one minimizing the total travel distance (min-sum), optimally in linear time. We also consider a query version of this problem for the min-max variant. We can preprocess a simple n-gon in linear time so that the minimum of the longer distance the two persons travel can be computed in O(log(2) n) time for any two query positions s, t where the two persons start. (C) 2019 Elsevier B.V. All rights reserved.
URI
http://oasis.postech.ac.kr/handle/2014.oak/100366
ISSN
0925-7721
Article Type
Article
Citation
COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, vol. 84, page. 12 - 21, 2019-11
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 AHN, HEE KAP
Dept of Computer Science & Enginrg
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