Exact algorithms and APX-hardness results for geometric packing and covering problems
نویسندگان
چکیده
منابع مشابه
Exact algorithms and APX-hardness results for geometric packing and covering problems
We study several geometric set cover and set packing problems involving configurations of points and geometric objects in Euclidean space. We show that it is APX-hard to compute a minimum cover of a set of points in the plane by a family of axis-aligned fat rectangles, even when each rectangle is an ǫ-perturbed copy of a single unit square. We extend this result to several other classes of obje...
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We study several geometric set cover problems in which the goal is to compute a minimum cover of a given set of points in Euclidean space by a family of geometric objects. We give a short proof that this problem is APX-hard when the objects are axis-aligned fat rectangles, even when each rectangle is an ǫ-perturbed copy of a single unit square. We extend this result to several other classes of ...
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Bansal and Sviridenko [4] proved that there is no asymptotic PTAS for 2-dimensional Orthogonal Bin Packing (without rotations), unless P = NP. We show that similar approximation hardness results hold for several 2and 3-dimensional rectangle packing and covering problems even if rotations by ninety degrees are allowed. Moreover, for some of these problems we provide explicit lower bounds on asym...
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In this paper, we study the Generalized Bin Covering problem. For this problem an exact algorithm is introduced which can nd optimal solution for small scale instances. To nd a solution near optimal for large scale instances, a heuristic algorithm has been proposed. By computational experiments, the eciency of the heuristic algorithm is assessed.
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در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2014
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2012.04.001