Split Packing: Algorithms for Packing Circles with Optimal Worst-Case Density
نویسندگان
چکیده
منابع مشابه
Split Packing: An Algorithm for Packing Circles with Optimal Worst-Case Density
In the circle packing problem for triangular containers, one asks whether a given set of circles can be packed into a given triangle. Packing problems like this have been shown to be NP-hard. In this paper, we present a new sufficient condition for packing circles into any right or obtuse triangle using only the circles’ combined area: It is possible to pack any circle instance whose combined a...
متن کاملSplit Packing: An Algorithm for Packing Circles with up to Critical Density
In the classic circle packing problem, one asks whether a given set of circles can be packed into the unit square. This problem is known to be NP-hard. In this thesis, we present a new sufficient condition using only the circles’ combined area: It is possible to pack any circle instance with a combined area of up to ≈53.90% of the square’s area. This area condition is tight, in the sense that f...
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The Split Packing algorithm [14, 24] is an offline algorithm that packs a set of circles into shapes (triangles and squares) at an optimal packing density. In this paper, we develop an online alternative to Split Packing to handle an online sequence of insertions and deletions, where the algorithm is allowed to reallocate circles into new positions at a cost proportional to their areas. The alg...
متن کاملGreedy algorithms for packing unequal circles into a rectangular container
In this paper, we study the problem of packing unequal circles into a 2D rectangular container. We solve this problem by proposing two greedy algorithms. The first algorithm, denoted by B1.0, selects the next circle to place according to the maximum hole degree rule, which is inspired from human activity in packing. The second algorithm, denoted by B1.5, improves B1.0 with a self look-ahead sea...
متن کاملPacking circles within ellipses
The problem of packing circles within ellipses is considered in the present paper. A new parametrization is employed by means of which the ellipse is represented by a rectangle. Algorithms with global convergence properties are presented. Numerical experiments are exhibited.
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2018
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-018-0020-2