Triangulating a polygon in parallel

Triangulating a Polygon in Parallel

In this paper we present a.n efficient pa.ra.Ilel algorithm. for polygon tria.ngu.Ia.tion. The algo-rithm we present runs in O(logn) time using D(n) processors, which is optimal if the polygon is allowed to contain holes. This improves the previous parallel complexity bounds for this problem by a log n factor. If we are also given a trapezoidal decomposition of the polygon as input, then we can...

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