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We propose an extremely simple approximation scheme for computing shortest paths on the surface of a convex polytope in three dimensions. Given a convex polytope P with n vertices and two points p, q on its surface, let dp(p,q) denote the shortest path distance between p and q on the surface of P. Our algorithm produces a path of length at most 2dp(p,q) in time O(n). Extending this result, we can...
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