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Computational geometry seminar: Computing the L1 Geodesic Diameter and Center of a Polygonal Domain

25/02/2016 de 13:00 a 14:00
Room S215 Omega Building, Campus Nord UPC
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Room S215 Omega Building, Campus Nord UPC (equiv.: Room 215 Floor Speaker:**Matias Korman Tokuyama Laboratory, Tohoku University (Japan)

Abstract: For a polygonal domain of h holes with a total of n vertices, we present algorithms that compute the L1 geodesic diameter in O(n^2+h^4) time and the L1 geodesic center in O((n^4+n2 h^4)α(n)) time, where α(·) denotes the inverse Ackermann function. No algorithms were known for these problems before. For the Euclidean counterpart, the best algorithms compute the geodesic diameter in O(n^7.73) or O(n^7(h + log n)) time, and compute the geodesic center in O(n^12+ε) time. Therefore, our algorithms are much faster than the algorithms for the Euclidean problems. Our algorithms are based on several interesting observations on L1 shortest paths in polygonal domains. 

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