Balancing graph Voronoi diagrams

Shinichi Honide*, Michael E. Houle, Christian Sommer

*この研究の対応する著者

研究成果: Conference contribution

9 被引用数 (Scopus)

抄録

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.

本文言語English
ホスト出版物のタイトル6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009
ページ183-191
ページ数9
DOI
出版ステータスPublished - 2009 12月 1
外部発表はい
イベント6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009 - Copenhagen, Denmark
継続期間: 2009 6月 232009 6月 26

出版物シリーズ

名前6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009

Other

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

ASJC Scopus subject areas

  • 情報システム
  • 生体医工学
  • 応用数学

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