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Querying Two Boundary Points for Shortest Paths in a Polygonal Domain

(Extended Abstract)
  • Sang Won Bae
  • Yoshio Okamoto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5878)

Abstract

We consider a variant of two-point Euclidean shortest path query problem: given a polygonal domain, build a data structure for two-point shortest path query, provided that query points always lie on the boundary of the domain. As a main result, we show that a logarithmic-time query for shortest paths between boundary points can be performed using \(\tilde{O}(n^5)\) preprocessing time and \(\tilde{O}(n^5)\) space where n is the number of corners of the polygonal domain and the \(\tilde{O}\)-notation suppresses the polylogarithmic factor. This is realized by observing a connection between Davenport-Schinzel sequences and our problem in the parameterized space. We also provide a tradeoff between space and query time; a sublinear time query is possible using O(n 3 + ε ) space. Our approach also extends to the case where query points should lie on a given set of line segments.

Keywords

Short Path Grid Cell Query Point Surface Patch Algebraic Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Sang Won Bae
    • 1
  • Yoshio Okamoto
    • 2
  1. 1.Department of Computer Science and EngineeringPOSTECHPohangKorea
  2. 2.Graduate School of Information Science and EngineeringTokyo Institute of TechnologyTokyoJapan

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