#### Title

Approximate Shortest Paths in Polygons with Violations

#### Article Type

Research Article

#### Publication Title

International Journal of Computational Geometry and Applications

#### Abstract

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.

#### First Page

79

#### Last Page

95

#### DOI

10.1142/S0218195920500041

#### Publication Date

3-1-2020

#### Recommended Citation

Dutta, Binayak and Roy, Sasanka, "Approximate Shortest Paths in Polygons with Violations" (2020). *Journal Articles*. 358.

https://digitalcommons.isical.ac.in/journal-articles/358