Proximity Constraints and Representable Trees,
Abstract
This paper examines an infinite family of proximity drawings of graphs called open and closed B-drawings, first defined by Kirkpatrick and Radke in the context of computational morphology. Such proximity drawings include as special cases the well-known Gabriel, relative neighborhood and strip drawings. Complete characterizations of those trees that admit open B-drawings for 0 <= B <= 1/(1-cos(2pi/5)) and 1/cos(2pi/5) < B < infinity or closed B-drawings for 0 <= B < 1/(1-cos(2pi/5)) and 1/cos(2pi/5) <= B <= infinity are given, as well as partial characterizations for other values of B. For the intervals of B in which complete characterizations are given, it can be determined in linear time whether a tree admits an open or closed B-drawing, and, if so, such a drawing can be computed in linear time in the real RAM model. Finally, a complete characterization of all graphs which admit closed strip drawings is given.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1996
- Accession Number
- ADA318674
Entities
People
- Giuseppe Di Battista
- Giuseppe Liotta
- Prosenjit Bose
- William Lenhart
Organizations
- Brown University