, Volume 81, Issue 7, pp 2829–2856 | Cite as

A New Balanced Subdivision of a Simple Polygon for Time-Space Trade-Off Algorithms

  • Eunjin Oh
  • Hee-Kap AhnEmail author


Given a read-only memory for input and a write-only stream for output, an s-workspace algorithm, for a positive integer parameter s, is an algorithm using only O(s) words of workspace in addition to the memory for the input. In this paper, we present an \(O(n^2/s)\)-time s-workspace algorithm for subdividing a simple n-gon into \(O(\min \{n/s,s\})\) subpolygons of complexity \(O(\max \{n/s,s\})\). As applications of the subdivision, the previously best known time-space trade-offs for the following three geometric problems are improved immediately by adopting the proposed subdivision: (1) computing the shortest path between two points inside a simple n-gon, (2) computing the shortest-path tree from a point inside a simple n-gon, (3) computing a triangulation of a simple n-gon. In addition, we improve the algorithm for problem (2) further by applying different approaches depending on the size of the workspace.


Time-space trade-off Balanced subdivision Simple polygon Shortest path Shortest path tree Triangulation 



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Max Planck Institute for InformaticsSaarbrückenGermany
  2. 2.Department of Computer Science and EngineeringPOSTECHPohangKorea

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