Witness (Delaunay) graphs

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Abstract

Proximity graphs are used in several areas in which a neighborliness relationship for input data sets is a useful tool in their analysis, and have also received substantial attention from the graph drawing community, as they are a natural way of implicitly representing graphs. However, as a tool for graph representation, proximity graphs have some limitations that may be overcome with suitable generalizations.

We introduce a generalization, witness graphs, that encompasses both the goal of more power and flexibility for graph drawing issues and a wider spectrum for neighborhood analysis. We study in detail two concrete examples, both related to Delaunay graphs, and consider as well some problems on stabbing geometric objects and point set discrimination, that can be naturally described in terms of witness graphs.

Keywords

Proximity graphs
Delaunay graph
Graph drawing
Witness graphs

Cited by (0)

1

Research partially supported by a grant from the U.S.–Israel Binational Science Foundation and NSF Grant CCF-08-30691. Research by B.A. also partially supported by NSA MSP Grant H98230-06-1-0016.

2

Partially supported by projects MEC MTM2006-01267, MTM2009-07242, Gen. Catalunya DGR 2005SGR00692 and 2009SGR1040.