Voronoi diagrams on periodic graphs

Norie Fu, Hiroshi Imai, Sonoko Moriyama

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

6 Citations (Scopus)

Abstract

A periodic graph models various natural and art- ficial periodic patterns with repetitions of a given static graph, and have vast applications in crystallography, scheduling, VLSI circuits and systems of uniform recurrence equations. This paper considers a graph Voronoi diagram for a given subset of vertices on a periodic graph. The simplest two-dimensional periodic graph is a square lattice, and the Voronoi diagram on the lattice geometrically corresponds to the L1 Voronoi diagram in the plane. We extend this geometric relation for the two- dimensional periodic graphs, including the honeycomb lattice, kagome lattice and two-dimensional periodic graph with small static graph. For these graphs, the graph Voronoi diagram can be represented implicitly by Voronoi diagrams with respect to appropriate convex-distance functions with extra elaborations.

Original languageEnglish
Title of host publicationISVD 2010 - 7th International Symposium on Voronoi Diagrams in Science and Engineering
Pages189-198
Number of pages10
DOIs
Publication statusPublished - 2010
Event7th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2010 - Quebec City, QC, Canada
Duration: 2010 Jun 282010 Jun 30

Publication series

NameISVD 2010 - 7th International Symposium on Voronoi Diagrams in Science and Engineering

Other

Other7th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2010
CountryCanada
CityQuebec City, QC
Period10/6/2810/6/30

Keywords

  • Graph Voronoi diagrams
  • Periodic graphs
  • Shortest paths

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Fingerprint Dive into the research topics of 'Voronoi diagrams on periodic graphs'. Together they form a unique fingerprint.

Cite this