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Efficient External Memory Algorithm for Planar Decomposition Simplification

Simplification algorithm for planar decomposition utilizing external memory efficiency, preserving planarity and homotopy of line strings while maintaining boundaries. The algorithm simplifies line strings based on face weights and forward edges. It is highly efficient in practice and preserves the XY constraint. Developed at MADALGO, Aarhus University.

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Efficient External Memory Algorithm for Planar Decomposition Simplification

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  1. Jakob Truelsen Aarhus University Jungwoo Yang Aarhus University Simplification of Planar Decomposition • External memory algorithm • Simplify line strings containing only nodes of degree two. • The weight of a face is the number of segments on it. • Line strings are simplified by the heaviest of the two faces containing it. • Forward edges for faces to all heavier neighbours. • Line strings are simplified by internal algorithm. 7 6 5 9 6 • The number of forwarded segments is at most 3n by duality of planar graph and arboricity[2, 3]. • This algorithm requires O(SORT(n)) I/Os. • Highly efficient in practice. • Properties 3 5 • Two distinct simplifications do not intersect if each simplification does not intersect with any segments simplified to the other simplification. • lnternal memory algorithm • >xy • Given all segments of two adjacent faces, simplify segments shared by the two faces. • The simplification does not intersect with any • segments of the two faces. (Preserving planarity) • The simplification preserves homotopy of segments. • The simplification does not violate xy-constraint. • Assumption • Simplification is done using Douglas Peucker. • Candidate segments are checked for intersection • with boundary using a trapezoidal decomposition. • Candidate segments are checked for self intersection using another trapezoidal decomposition. MADALGO – Center for Massive Data Algorithmics, a Center of the Danish National Research Foundation

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