The Hausdorff Voronoi diagram of clusters of points in the plane is a generalization of Voronoi diagrams based on the Hausdorff distance function. Its combinatorial complexity is O(n+m), where n is the total number of points and m is the number of crossings between the input clusters (formula presented) the number of clusters is k. We present efficient algorithms to construct this diagram via the randomized incremental construction (RIC) framework For non-crossing clusters (m=0), our algorithm runs in expected (formula presented) time and deterministic O(n) space. For arbitrary clusters the algorithm runs in expected (formula presented) space. The two algorithms can be combined in a crossing-oblivious scheme within the same bounds. We show how to apply the RIC framework efficiently to handle non-standard characteristics of generalized Voronoi diagrams, including sites (and bisectors) of non-constant complexity, sites that are not enclosed in their Voronoi regions, empty Voronoi regions, and finally, disconnected bisectors and Voronoi regions. The diagram finds direct applications.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 23rd International Conference, COCOON 2017, Proceedings
EditorsYixin Cao, Jianer Chen
PublisherSpringer Nature
Pages321-332
Number of pages12
ISBN (Print)9783319623887
DOIs
StatePublished - 1 Jan 2017
Externally publishedYes
Event23rd International Conference on Computing and Combinatorics, COCOON 2017 - Hong Kong, China
Duration: 3 Aug 20175 Aug 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10392 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference23rd International Conference on Computing and Combinatorics, COCOON 2017
Country/TerritoryChina
CityHong Kong
Period3/08/175/08/17

    Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

ID: 38614848