Proximity Constraints and Representable Trees,
BROWN UNIV PROVIDENCE RI DEPT OF COMPUTER SCIENCE
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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 11-cos2pi5 and 1cos2pi5 B infinity or closed B-drawings for 0 B 11-cos2pi5 and 1cos2pi5 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.
- Operations Research