Approximate Shortest Paths in Polygons with Violations

Article Type

Research Article

Publication Title

International Journal of Computational Geometry and Applications


We study the shortest k-violation path problem in a simple polygon. Let P be a simple polygon in 2 with n vertices and let s,t be a pair of points in P. Let int(P) represent the interior of P. Let P = 2(P) represent the exterior of P. For an integer k ≥ 0, the shortest k-violation path problem in P is the problem of computing the shortest path from s to t in P, such that at most k path segments are allowed to be in P. The subpaths of a k-violation path are not allowed to bend in P. For any k, we present a (1 + 2) factor approximation algorithm for the problem that runs in O(n2σ2klog n2σ2 + n2σ2k) time. Here σ = O(log(L r)) and, L, r are geometric parameters.

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