An algorithm for the MaxMin area triangulation of a convex polygon

Given a convex polygon in the plane, we are interested in triangulations of its interior, i.e. maximal sets of nonintersecting diagonals that subdivide the interior of the polygon into triangles. The MaxMin area triangulation is the triangulation of the polygon that maximizes the area of the smallest area triangle in the triangulation. There exists a dynamic programming algorithm that computes the optimal triangulation with respect to a number of optimality criteria in Θ(n3 ) time and Θ(n2 ) space, [4]. We present an algorithm that constructs the MaxMin area triangulation of a convex polygon in O(n2 log n log log n) time and O(n2 ) space. The algorithm is based on the dynamic programming approach and uses a number of problem-specific geometric properties that are established within the paper.

• Type: Conference
• Year: 2003
• Where: CCCG
• Authors: J. Mark Keil, Tzvetalin S. Vassilev
• Keywords: CCCG 2003, CCCG 2007, Convex Polygon, MaxMin Area Triangulation, Polygon