Triangulating a simple polygon in linear time

Triangulating a Simple Polygon in Linear Time

Triangulating a simple polygon has been one of the most outstanding open problems in two-dimensional computational geometry. It is a basic primitive in computer graphics and, generally, seems the natural preprocessing step for most nontrivial operations on simple polygons [5,13]. Recall that to triangulate a polygon is t o partition it into triangles without adding any new vertices. Despite its...

Time-Space Trade-offs for Triangulating a Simple Polygon

An s-workspace algorithm is an algorithm that has read-only access to the values of the input, write-only access to the output, and only uses O(s) additional words of space. We present a randomized s-workspace algorithm for triangulating a simple polygon P of n vertices that runs in O(n/s+ n logn log(n/s)) expected time using O(s) variables, for any s ≤ n. In particular, when s ≤ n logn log5 lo...

Time-Space Trade-off Algorithms for Triangulating a Simple Polygon∗

An s-workspace algorithm is an algorithm that has read-only access to the values of the input, write-only access to the output, and only uses O(s) additional words of space. We present a randomized s-workspace algorithm for triangulating a simple polygon P of n vertices that runs in O(n/s+ n logn log(n/s)) expected time using O(s) variables, for any s ≤ n. In particular, when s ≤ n logn log5 lo...

A Randomized Algorithm for Triangulating a Simple Polygon in Linear Time

Correction to "A Linear-Time Algorithm for Triangulating Simple Polygons"

The analysis showing that our triangulation algorithm runs in linear time is incorrect, and indeed the algorithm does not run in linear time in the worst case. So far we have been unable to obtain a linear-time algorithm for the triangulation problem. We have been able to obtain an 0 (n loglogn)-time algorithm, however. The details are described in ,cAn O(n loglogn)-Time Algorithm for Triangula...