Pii: S0925-7721(00)00016-x

LMT-skeleton heuristics for several new classes of optimal triangulations

Given a planar point set, we consider three classes of optimal triangulations: (1) the minimum weight triangulation with angular constraints (constraints on the minimum angle and the maximum angle in a triangulation), (2) the angular balanced triangulation which minimizes the sum of the ratios of the maximum angle to the minimum angle for each triangle and (3) the area balanced triangulation wh...

Pii: S0925-7721(99)00016-4

Define a graph GT (n) with one node for each triangulation of a convex n-gon. Place an edge between each pair of nodes that differ by a single flip: two triangles forming a quadrilateral are exchanged for the other pair of triangles forming the same quadrilateral. In this paper we introduce a tree of all triangulations of polygons with any number of vertices which gives a unified framework in w...

Pii: S0925-7721(00)00010-9

We improve previous lower bounds on the number of simple polygonizations, and other kinds of crossing-free subgraphs, of a set of N points in the plane by analyzing a suitable configuration. We also prove that the number of crossing-free perfect matchings and spanning trees is minimum when the points are in convex position.  2000 Elsevier Science B.V. All rights reserved.

Minimal Tangent Visibility Graphs

Computing simple paths among obstacles

Given a set X of points in the plane, two distinguished points s; t 2 X, and a set of obstacles represented by line segments, we wish to compute a simple polygonal path from s to t that uses only points in X as vertices and avoids the obstacles in. We present two results: (1) We show that nding such simple paths among arbitrary obstacles is NP-complete. (2) We give a polynomial-time algorithm t...