Time–space trade-offs for triangulations and Voronoi diagrams

Matias Korman, Wolfgang Mulzer, André van Renssen, Marcel Roeloffzen, Paul Seiferth, Yannik Stein

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Let S be a planar n-point set. A triangulation for S is a maximal plane straight-line graph with vertex set S. The Voronoi diagram for S is the subdivision of the plane into cells such that all points in a cell have the same nearest neighbor in S. Classically, both structures can be computed in O(nlog⁡n) time and O(n) space. We study the situation when the available workspace is limited: given a parameter s∈{1,…,n}, an s-workspace algorithm has read-only access to an input array with the points from S in arbitrary order, and it may use only O(s) additional words of Θ(log⁡n) bits for reading and writing intermediate data. The output should then be written to a write-only structure. We describe a deterministic s-workspace algorithm for computing an arbitrary triangulation of S in time O(n2/s+nlog⁡nlog⁡s) and a randomized s-workspace algorithm for finding the Voronoi diagram of S in expected time O((n2/s)log⁡s+nlog⁡slog⁡s).

Original languageEnglish
Pages (from-to)35-45
Number of pages11
JournalComputational Geometry: Theory and Applications
Volume73
DOIs
Publication statusPublished - 2018 Aug

Keywords

  • Randomized algorithm
  • Time–space trade-off
  • Triangulation
  • Voronoi diagram

ASJC Scopus subject areas

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

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  • Cite this

    Korman, M., Mulzer, W., van Renssen, A., Roeloffzen, M., Seiferth, P., & Stein, Y. (2018). Time–space trade-offs for triangulations and Voronoi diagrams. Computational Geometry: Theory and Applications, 73, 35-45. https://doi.org/10.1016/j.comgeo.2017.01.001