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2010

Algorithms for Approximate Shortest Path Queries on Weighted Polyhedral Surfaces

8 years 11 months ago
Algorithms for Approximate Shortest Path Queries on Weighted Polyhedral Surfaces
We consider the well known geometric problem of determining shortest paths between pairs of points on a polyhedral surface P, where P consists of triangular faces with positive weights assigned to them. The cost of a path in P is defined to be the weighted sum of Euclidean lengths of the sub-paths within each face of P. We present query algorithms that compute approximate distances and/or approximate shortest paths on P. Our all-pairs query algorithms take as input an approximation parameter (0, 1) and a query time parameter q, in a certain range, and builds a data structure APQ(P, ; q), which is then used for answering -approximate distance queries in O(q) time. As a building block of the APQ(P, ; q) data structure, we develop a single source query data structure SSQ(a; P, ) that can answer -approximate distance queries from a fixed point a to any query point on P in logarithmic time. Our algorithms answer shortest path queries in weighted surfaces, which is an important extension,...
Lyudmil Aleksandrov, Hristo Djidjev, Hua Guo, Anil
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2010
Where DCG
Authors Lyudmil Aleksandrov, Hristo Djidjev, Hua Guo, Anil Maheshwari, Doron Nussbaum, Jörg-Rüdiger Sack
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