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A Categorical Approach for Parallel Delaunay Mesh Generation

 

Stratos Prassidis and Nikos Chrisochoides.

 

Published in Algebraic Topological Methods in Computer Science in 2004

 

Abstract

 

One of the challenges for stable parallel Delaunay mesh generations is concurrency. Partial order is a tool for maintaining stability in the context of concurrency. On the other hand, partially ordered sets are one of the basic examples of categories. We will develop a theoretical framework using category theory to study the stability of parallel 2-dimensional Delaunay triangulations based on the Bowyer-Watson kernel. Ultimately the triangulation becomes the homotopy colimit of certain functors.