### 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(nlogn) 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(logn) 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(n^{2}/s+nlognlogs) and a randomized s-workspace algorithm for finding the Voronoi diagram of S in expected time O((n^{2}/s)logs+nlogslog^{⁎}s).

Original language | English |
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Pages (from-to) | 35-45 |

Number of pages | 11 |

Journal | Computational Geometry: Theory and Applications |

Volume | 73 |

DOIs | |

Publication status | Published - 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

*Computational Geometry: Theory and Applications*,

*73*, 35-45. https://doi.org/10.1016/j.comgeo.2017.01.001