We present an approximation algorithm that, given a simple, possibly nonconvex polyhedron P with n vertices in R 3 , and two points s and t on its surface @P , constructs a path on @P between s and t whose length is at most 7(1 + ") , where is the length of the shortest path between s and t on @P , and " > 0 is an arbitararily small positive constant. The algorithm runs in O(n 5=3 log 5=3 n) time. We also present a slightly faster algorithm that runs in O(n 8=5 log 8=5 n) time and returns a path whose length is at most 15(1 + ") .
Varadarajan and Agarwal REF presented two algorithms for computing a path on nonconvex polyhedra, one running in O(n 5/3 log 5/3 n) time and a slightly faster one running in O(n 8/5 log 8/5 n) time.
Approximating Shortest Paths on a Nonconvex Polyhedron
In Proc. 38th Annu. IEEE Sympos. Found. Comput. Sci
Mathematics Computer Science