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 journalArticlepeer-review

2 Citations (Scopus)


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
Publication statusPublished - 2018 Aug


  • 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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