COCOON 1998: Computing and Combinatorics pp 25-34

# Maximum Weight Triangulation and Its Application on Graph Drawing

• Cao An Wang
• Francis Y. Chin
• Bo Ting Yang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1449)

## Abstract

In this paper, we investigate the maximum weight triangulation of a polygon inscribed in a circle (simply inscribed polygon). A complete characterization of maximum weight triangulation of such polygons has been obtained. As a consequence of this characterization, an O(n 2) algorithm for finding the maximum weight triangulation of an inscribed n-gon is designed. In case of a regular polygon, the complexity of this algorithm can be reduced to O(n). We also show that a tree admits a maximum weight drawing if its internal node connects at most 2 non-leaf nodes. The drawing can be done in O(n) time. Furthermore, we prove a property of maximum planar graphs which do not admit a maximum weight drawing on any set of convex points.

## Keywords

Span Tree Maximum Weight Minimum Weight Boundary Edge Regular Polygon
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Cao An Wang
• 1
• Francis Y. Chin
• 2
• Bo Ting Yang
• 2
1. 1.Department of Computer ScienceMemorial University of NewfoundlandSt. John’sCanada
2. 2.Department of Computer ScienceUniversity of Hong KongHong Kong