Maintaining reeb graphs of triangulated 2-manifolds
© Pankaj K. Agarwal, Kyle Fox and Abhinandan Nath. Let M be a triangulated, orientable 2-manifold of genus g without boundary, and let h be a height function over M that is linear within each triangle. We present a kinetic data structure (KDS) for maintaining the Reeb graph R of h as the heights of M’s vertices vary continuously with time. Assuming the heights of two vertices of M become equal only O(1) times, the KDS processes O((? + g)n polylog n) events; n is the number of vertices in M, and ? is the number of external events which change the combinatorial structure of R. Each event is processed in O(log 2 n) time, and the total size of our KDS is O(gn). The KDS can be extended to maintain an augmented Reeb graph as well.
Agarwal, PK; Fox, K; Nath, A
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International Standard Book Number 13 (ISBN-13)
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