A Practical Algorithm for Approximating Shortest Weighted Path between a Pair of Points on Polyhedral Surface

This paper presents an approximation algorithm for finding minimum cost path between two points on the surface of a weighted polyhedron in 3D. It terminates in finite time. For a restricted class of polyhedron better approximation bound can be obtained.

[1]  Pankaj K. Agarwal,et al.  Approximating Shortest Paths on a Nonconvex Polyhedron , 2000, SIAM J. Comput..

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

[3]  Jörg-Rüdiger Sack,et al.  Approximating Shortest Paths on Weighted Polyhedral Surfaces , 2001, Algorithmica.

[4]  Joseph S. B. Mitchell,et al.  The Discrete Geodesic Problem , 1987, SIAM J. Comput..

[5]  Joseph S. B. Mitchell,et al.  The weighted region problem: finding shortest paths through a weighted planar subdivision , 1991, JACM.

[6]  Sanjiv Kapoor,et al.  Efficient computation of geodesic shortest paths , 1999, STOC '99.

[7]  Mark Ziegelmann.  Constrained shortest paths and related problems , 2001 .

[8]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[9]  J. Sack,et al.  Handbook of computational geometry , 2000 .

[10]  Yijie Han,et al.  Shortest paths on a polyhedron , 1996, Int. J. Comput. Geom. Appl..

[11]  Yijie Han,et al.  Shortest paths on a polyhedron , 1990, SCG '90.

[12]  Jörg-Rüdiger Sack,et al.  Approximating weighted shortest paths on polyhedral surfaces , 1997, SCG '97.

[13]  Joseph S. B. Mitchell,et al.  A new algorithm for computing shortest paths in weighted planar subdivisions (extended abstract) , 1997, SCG '97.

[14]  Stefan Arnborg,et al.  Algorithm Theory — SWAT'98 , 1998, Lecture Notes in Computer Science.

[15]  Jörg-Rüdiger Sack,et al.  An Improved Approximation Algorithm for Computing Geometric Shortest Paths , 2003, FCT.

[16]  Pankaj K. Agarwal,et al.  Computing Approximate Shortest Paths on Convex Polytopes , 2001, Algorithmica.

[17]  Jörg-Rüdiger Sack,et al.  An epsilon-Approximation for Weighted Shortest Paths on Polyhedral Surfaces , 1998, SWAT.

[18]  Jörg-Rüdiger Sack,et al.  Approximation algorithms for geometric shortest path problems , 2000, STOC '00.

[19]  Micha Sharir,et al.  On Shortest Paths in Polyhedral Spaces , 1986, SIAM J. Comput..