Computing a visibility polygon using few variables

Luis Barba, Matias Korman, Stefan Langerman, Rodrigo I. Silveira

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

Abstract

We present several algorithms for computing the visibility polygon of a simple polygon P of n vertices (out of which r are reflex) from a viewpoint inside P, when P resides in read-only memory and only few working variables can be used. The first algorithm uses a constant number of variables, and outputs the vertices of the visibility polygon in O(nr̄) time, where r̄ denotes the number of reflex vertices of P that are part of the output. Whenever we are allowed to use O(s) variables, the running time decreases to O(nr2 s+nlog2r) (or O(nr2s+nlogr) randomized expected time), where s∈O(logr). This is the first algorithm in which an exponential space-time trade-off for a geometric problem is obtained.

Original languageEnglish
Pages (from-to)918-926
Number of pages9
JournalComputational Geometry: Theory and Applications
Volume47
Issue number9
DOIs
Publication statusPublished - 2014 Oct
Externally publishedYes

Keywords

  • Computational geometry
  • Memory-constrained algorithms
  • Simple polygon
  • Time-space-trade-off visibility

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

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