Inducing Polygons of Line Arrangements

We show that an arrangement \(\mathcal{A}\) of n lines in general position in the plane has an inducing polygon of size O(n). Additionally, we present a simple algorithm for finding an inducing n-path for \(\mathcal {A}\) in O(nlogn) time and an algorithm that constructs an inducing n-gon for a special class of line arrangements within the same time bound.

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