On Romeo and Juliet Problems: Minimizing Distance-to-Sight

Authors Hee-Kap Ahn, Eunjin Oh, Lena Schlipf, Fabian Stehn, Darren Strash

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Author Details

Hee-Kap Ahn
  • Department of Computer Science and Engineering, POSTECH, Pohang, South Korea
Eunjin Oh
  • Department of Computer Science and Engineering, POSTECH, Pohang, South Korea
Lena Schlipf
  • Theoretische Informatik, FernUniversität in Hagen, Hagen, Germany
Fabian Stehn
  • Institut für Informatik, Universität Bayreuth, Bayreuth, Germany
Darren Strash
  • Department of Computer Science, Colgate University, Hamilton, USA

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Hee-Kap Ahn, Eunjin Oh, Lena Schlipf, Fabian Stehn, and Darren Strash. On Romeo and Juliet Problems: Minimizing Distance-to-Sight. In 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 101, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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 these persons 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 where the two persons lie.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Mathematics of computing → Paths and connectivity problems
  • Visibility polygon
  • shortest-path
  • watchman problems


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