Largest inscribed rectangles in convex polygons

We consider approximation algorithms for the problem of computing an inscribed rectangle having largest area in a convex polygon on n vertices. If the order of the vertices of the polygon is given, we present a randomized algorithm that computes an inscribed rectangle with area at least (1/ε) times the optimum with probability t in time O(1εlogn) for any constant t<1. We further give a deterministic approximation algorithm that computes an inscribed rectangle of area at least (1-ε) times the optimum in running time O(1 ε2logn) and show how this running time can be slightly improved.

Schlagworte

Approximation algorithms

Geometric algorithms

Inscribed rectangles in polygons

Largest area rectangle

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Largest inscribed rectangles in convex polygons