Maximum weight triangulation and graph drawing

In this paper, we investigate the maximum weight triangulation of a convex polygon and its application to graph drawing. We can find the maximum weight triangulation of a special n-gon which inscribed on a circle in O(n 2) time. The complexity of this algorithm can be reduced to O(n) if the polygon is regular. The algorithm also produces a triangulation approximating the maximum weight triangulation of a convex n-gon with weight ratio 0.5. We further show that a tree always admits a maximum weight drawing if the internal nodes of the tree connect to at most 2 non-leaf nodes, and the drawing can be done in O(n) time. Finally, we prove a property of maximum planar graphs which do not admit a maximum weight drawing on any convex point set.