### 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 each cell has the same nearest neighbors in S. Classically, both structures can be computed in O(n log 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 a triangulation of S in time O(n^{2}/s + n log n log s) and a randomized s-workspace algorithm for finding the Voronoi diagram of S in expected time O((n^{2}/s) log s + n log s log^{∗} s).

Original language | English |
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Title of host publication | Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings |

Editors | Frank Dehne, Jorg-Rudiger Sack, Ulrike Stege |

Publisher | Springer Verlag |

Pages | 482-494 |

Number of pages | 13 |

ISBN (Print) | 9783319218397 |

DOIs | |

Publication status | Published - 2015 |

Event | 14th International Symposium on Algorithms and Data Structures, WADS 2015 - Victoria, Canada Duration: 2015 Aug 5 → 2015 Aug 7 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9214 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 14th International Symposium on Algorithms and Data Structures, WADS 2015 |
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Country | Canada |

City | Victoria |

Period | 15/8/5 → 15/8/7 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings*(pp. 482-494). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9214). Springer Verlag. https://doi.org/10.1007/978-3-319-21840-3_40