论文信息 - Flying over a polyhedral terrain

Flying over a polyhedral terrain

We consider the problem of computing shortest paths in three-dimensions in the presence of a single-obstacle polyhedral terrain, and present a new algorithm that for any p>=1, computes a ([email protected])-approximation to the L"p-shortest path above a polyhedral terrain in O([email protected]) time and O(nlogn) space, where n is the number of vertices of the terrain, and c=2^(^p^-^1^)^/^p. This leads to a FPTAS for the problem in L"1 metric, a ([email protected])-factor approximation algorithm in Euclidean space, and a 2-approximation algorithm in the general L"p metric.

Hamid Zarrabi-Zadeh

[1] Kenneth L. Clarkson,et al. Approximation algorithms for shortest path motion planning , 1987, STOC.

[2] Joseph S. B. Mitchell,et al. Geometric Shortest Paths and Network Optimization , 2000, Handbook of Computational Geometry.

[3] Joseph S. B. Mitchell,et al. L1 shortest paths among polygonal obstacles in the plane , 1992, Algorithmica.

[4] Joseph S. B. Mitchell,et al. Shortest Paths and Networks , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[5] John F. Canny,et al. New lower bound techniques for robot motion planning problems , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[6] Joseph S. B. Mitchell,et al. New results on shortest paths in three dimensions , 2004, SCG '04.

[7] David G. Kirkpatrick,et al. Pseudo Approximation Algorithms with Applications to Optimal Motion Planning , 2004, Discret. Comput. Geom..

[8] Christos H. Papadimitriou,et al. An Algorithm for Shortest-Path Motion in Three Dimensions , 1985, Inf. Process. Lett..

[9] Michael Ian Shamos,et al. Computational geometry: an introduction , 1985 .

[10] Subhash Suri,et al. An Optimal Algorithm for Euclidean Shortest Paths in the Plane , 1999, SIAM J. Comput..