Largest inscribed rectangles in convex polygons
نویسندگان
چکیده
منابع مشابه
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− ) times the optimum with probability t in time O( 1 log n) for any constant t < 1. We further give a dete...
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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 deterministic approximation algorithm that computes an inscribed rectangle of area at least 1− times the optimum in running time O( 1 log 1 log n). Furthermore, a randomized approximatio...
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We consider the following geometric optimization problem: find a maximum-area rectangle and a maximum-perimeter rectangle contained in a given convex polygon with n vertices. We give exact algorithms that solve these problems in time O(n). We also give (1 − ε)-approximation algorithms that take time O(ε−3/2 + ε−1/2 log n) for maximizing the area and O(ε−3 + ε−1 log n) for maximizing the perimeter.
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In many industrial and non-industrial applications, it is necessary to identify the largest inscribed rectangle in a certain shape. The problem is studied for convex and non-convex polygons. Another criterion is the direction of the rectangle: axis aligned or general. In this paper a heuristic algorithm is presented for finding the largest axis aligned inscribed rectangle in a general polygon. ...
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Suppose x̄ and s̄ lie in the interiors of a cone K and its dual K∗ respectively. We seek dual ellipsoidal norms such that the product of the radii of the largest inscribed balls centered at x̄ and s̄ and incribed in K and K∗ respectively is maximized. Here the balls are defined using the two dual norms. We provide a solution when the cones are symmetric, that is self-dual and homogeneous. This prov...
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ژورنال
عنوان ژورنال: Journal of Discrete Algorithms
سال: 2012
ISSN: 1570-8667
DOI: 10.1016/j.jda.2012.01.002