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- W2247847117 abstract "The problem of finding a collection of curves of minimum total length that meet all the lines intersecting a given polygon was initiated byMazurkiewicz in 1916. Such a collection forms an opaque barrier for the polygon. In 1991 Shermer proposed an exponential-time algorithm that computes an interior-restricted barrier made of segments for any given convex n-gon. He conjectured that the barrier found by his algorithm is optimal, however this was refuted recently by Provan et al. Here we give a Shermer like algorithm that computes an interior polygonal barrier whose length is at most 1.7168 times the optimal and that runs in O(n) time. As a byproduct, we also deduce upper and lower bounds on the approximation ratio of Shermer's algorithm." @default.
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- W2247847117 date "2014-09-02" @default.
- W2247847117 modified "2023-09-24" @default.
- W2247847117 title "Computing Opaque Interior Barriers `a la Shermer" @default.
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- W2247847117 doi "https://doi.org/10.4230/lipics.approx-random.2014.128" @default.
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