Balancing graph Voronoi diagrams

Shinichi Honiden, Michael E. Houle, Christian Sommer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

Many facility location problems are concerned with minimizing operation and transportation costs by partitioning territory into regions of similar size, each of which is served by a facility. For many optimization problems, the overall cost can be reduced by means of a partitioning into balanced subsets, especially in those cases where the cost associated with a subset is superlinear in its size. In this paper, we consider the problem of generating a Voronoi partition of a discrete graph so as to achieve balance conditions on the region sizes. Through experimentation, we first establish that the region sizes of randomly-generated graph Voronoi diagrams vary greatly in practice.We then show how to achieve a balanced partition of a graph via Voronoi site resampling. For bounded-degree graphs, where each of the n nodes has degree at most d, and for an initial randomly-chosen set of s Voronoi nodes, we prove that, by extending the set of Voronoi nodes using an algorithm by Thorup and Zwick, each Voronoi region has size at most 4dn/s+1 nodes, and that the expected size of the extended set of Voronoi nodes is at most 2s log n.

Original languageEnglish
Title of host publication6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009
Pages183-191
Number of pages9
DOIs
Publication statusPublished - 2009 Dec 1
Externally publishedYes
Event6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009 - Copenhagen, Denmark
Duration: 2009 Jun 232009 Jun 26

Other

Other6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009
CountryDenmark
CityCopenhagen
Period09/6/2309/6/26

Fingerprint

Voronoi
Voronoi Diagram
Balancing
Graph in graph theory
Costs
Vertex of a graph
Partitioning
Partition
Subset
Facility Location Problem
Resampling
Experimentation
Vary
Optimization Problem

Keywords

  • Balancing
  • Facility location
  • Graph Voronoi diagram
  • Territorial design

ASJC Scopus subject areas

  • Information Systems
  • Biomedical Engineering
  • Applied Mathematics

Cite this

Honiden, S., Houle, M. E., & Sommer, C. (2009). Balancing graph Voronoi diagrams. In 6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009 (pp. 183-191). [5362361] https://doi.org/10.1109/ISVD.2009.26

Balancing graph Voronoi diagrams. / Honiden, Shinichi; Houle, Michael E.; Sommer, Christian.

6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009. 2009. p. 183-191 5362361.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Honiden, S, Houle, ME & Sommer, C 2009, Balancing graph Voronoi diagrams. in 6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009., 5362361, pp. 183-191, 6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009, Copenhagen, Denmark, 09/6/23. https://doi.org/10.1109/ISVD.2009.26
Honiden S, Houle ME, Sommer C. Balancing graph Voronoi diagrams. In 6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009. 2009. p. 183-191. 5362361 https://doi.org/10.1109/ISVD.2009.26
Honiden, Shinichi ; Houle, Michael E. ; Sommer, Christian. / Balancing graph Voronoi diagrams. 6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009. 2009. pp. 183-191
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