Maximum weight triangulation and its application on graph drawing

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(n2) 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.