: Several new results in planar triangulations are presented. In particular, an O(N sq log N) time worst-case algorithm for the construction of the 'greedy' triangulation is presented, an improvement over the previously best-known construction in time O(N cu). The minimum weight triangulation (MWT) of a simple N-vertex polygon is shown to be constructible in time O(N cu). A local property of MWTs is proved, a side result of which is that the shortest edge between a pair of points must be in a MWT. Also, it is shown that the Delaunay Triangulation is not 'approximately optimal', and that the ratio of the total length of the Delaunay Triangulation of N points to that of the MWT can be large as roughly N/2. (Author)

New Results on Planar Triangulations.

Neither the greedy nor the delaunay triangulation of a planar point set approximates the optimal triangulation

The Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) has been under development at JPL for the past four years. During this time, a dedicated ground data-processing system has been designed and implemented to store and process the large amounts of data expected. This paper reviews the objectives of this ground data-processing system and describes the hardware. An outline of the data flow through the system is given, and the software and incorporated algorithms developed specifically for the systematic processing of AVIRIS data are described.

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AVIRIS Ground Data-Processing System

The paper addresses the problem of how to find the Greedy Triangulation (GT) efficiently in the average case. It is noted that the problem is open whether there exists an efficient approximation algorithm to the Optimum Triangulation. It is first shown how in the worst case, the GT may be obtained in time O(n to the 3) and space O(n). Attention is then given to how the algorithm may be slightly modified to produce a time O(n to the 2), space O(n) solution in the average case. Finally, it is mentioned that Gilbert has found a worst case solution using totally different techniques that require space O(n to the 2) and time O(n to the 2 log n).

A fast, space-efficient average-case algorithm for the 'Greedy' Triangulation of a point set, and a proof that the Greedy Triangulation is not approximately optimal

G. K. Manacher

Papers

A fast, space-efficient average-case algorithm for the 'Greedy' Triangulation of a point set, and a proof that the Greedy Triangulation is not approximately optimal