TY - GEN

T1 - Voronoi diagrams on periodic graphs

AU - Fu, Norie

AU - Imai, Hiroshi

AU - Moriyama, Sonoko

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Graph Voronoi diagrams

KW - Periodic graphs

KW - Shortest paths

UR - http://www.scopus.com/inward/record.url?scp=77955671136&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955671136&partnerID=8YFLogxK

U2 - 10.1109/ISVD.2010.26

DO - 10.1109/ISVD.2010.26

M3 - Conference contribution

AN - SCOPUS:77955671136

SN - 9780769541129

T3 - ISVD 2010 - 7th International Symposium on Voronoi Diagrams in Science and Engineering

SP - 189

EP - 198

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

T2 - 7th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2010

Y2 - 28 June 2010 through 30 June 2010

ER -