Approximate Euclidean Shortest Paths in Polygonal Domains

Authors R. Inkulu, Sanjiv Kapoor



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Author Details

R. Inkulu
  • Department of Computer Science & Engineering, IIT Guwahati, India
Sanjiv Kapoor
  • Department of Computer Science & Engineering, IIT Chicago, USA

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R. Inkulu and Sanjiv Kapoor. Approximate Euclidean Shortest Paths in Polygonal Domains. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ISAAC.2019.11

Abstract

Given a set P of h pairwise disjoint simple polygonal obstacles in R^2 defined with n vertices, we compute a sketch Omega of P whose size is independent of n, depending only on h and the input parameter epsilon. We utilize Omega to compute a (1+epsilon)-approximate geodesic shortest path between the two given points in O(n + h((lg n) + (lg h)^(1+delta) + (1/epsilon) lg(h/epsilon)))) time. Here, epsilon is a user parameter, and delta is a small positive constant (resulting from the time for triangulating the free space of P using the algorithm in [Bar-Yehuda and Chazelle, 1994]). Moreover, we devise a (2+epsilon)-approximation algorithm to answer two-point Euclidean distance queries for the case of convex polygonal obstacles.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Computational Geometry
  • Geometric Shortest Paths
  • Approximation Algorithms

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