Approximating Shortest Paths on a Nonconvex Polyhedron

  title={Approximating Shortest Paths on a Nonconvex Polyhedron},
  author={Rangachar Kasturi and Varadarajany and Kumar Pankaj and AgarwalzJuly},
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… CONTINUE READING
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