On the definition and the construction of pockets in macromolecules
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
The flow complex: a data structure for geometric modeling
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Alpha-shapes and flow shapes are homotopy equivalent
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Medial axis approximation and unstable flow complex
Proceedings of the twenty-second annual symposium on Computational geometry
The flow complex: A data structure for geometric modeling
Computational Geometry: Theory and Applications
Recursive geometry of the flow complex and topology of the flow complex filtration
Computational Geometry: Theory and Applications
Robust construction of the three-dimensional flow complex
Proceedings of the twenty-fourth annual symposium on Computational geometry
Reconstructing 3D compact sets
Computational Geometry: Theory and Applications
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We present a parallel algorithm and its implementation for computing the entire Hasse diagram of the flow complex of a point cloud in Euclidean space. Known algorithms for computing the flow complex in two and three dimensions compute the geometric realization of the flow complex and need to compute the Delaunay triangulation of the point cloud first. Our algorithm computes less information, namely only the Hasse diagram of the flow complex that is augmented with enough geometric information to allow the same topological multi-scale analysis of point cloud data as the alpha shape filtration without computing the Delaunay triangulation explicitly. We show experimental results for medium dimensions that demonstrate that our algorithm scales well with the number of available cores on a multicore architecture.