Constant-time algorithms for constrained triangulations on reconfigurable meshes

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Computer Science

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A number of applications in computer-aided manufacturing, CAD, and computer-aided geometric design ask for triangulating pieces of material with defects. These tasks are known collectively as constrained triangulations. Recently, a powerful architecture called the reconfigurable mesh has been proposed: In essence, a reconfigurable mesh consists of a mesh-connected architecture augmented by a dynamically reconfigurable bus system. The main contribution of this paper is to show that the flexibility of the reconfigurable mesh can be exploited for the purpose of obtaining constant-time algorithms for a number of constrained triangulation problems. These include triangulating a convex planar region containing any constant number of convex holes, triangulating a convex planar region in the presence of a collection of rectangular holes, and triangulating a set of ordered line segments. Specifically with a collection of O(n) such objects as input, our algorithms run in O(1) time on a reconfigurable mesh of size n/spl times/n. To the best of our knowledge, this is the first time constant time solutions to constrained triangulations are reported on this architecture.


This article was originally published in IEEE Transactions on Parallel and Distributed Systems. The full-text article from the publisher can be found here.

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IEEE Transactions on Parallel and Distributed Systems


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