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,...

• Type: Journal
• Year: 2010
• Where: DCG
• Authors: Lyudmil Aleksandrov, Hristo Djidjev, Hua Guo, Anil Maheshwari, Doron Nussbaum, Jörg-Rüdiger Sack
• Keywords: Algorithms, DCG 2010, Query Algorithms, Shortest Paths