## Finding a Hausdorff Core of a Polygon: On Convex Polygon Containment with Bounded Hausdorff Distance

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## Abstract

Given a simple polygon P,
we consider the problem of finding a convex polygon Q contained in P
that minimizes H(P,Q), where H denotes Hausdorff distance.
We call such a polygon Q a Hausdorff core of P.
We describe polynomial-time approximations for both the minimization and decision
versions of the Hausdorff core problem, and we provide an argument supporting the hardness of the problem.