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1,299
Using global constraints for rectangle packing
 In Proceedings of the first Workshop on Bin Packing and Placement Constraints BPPC’08
, 2008
"... Abstract. In this paper we solve the optimal rectangle packing problem using Cumulative and Disjoint2 constraints in SICStus Prolog with a novel decomposition method, together with a specialized search routine and various model enhancements. We improve the best known runtimes by up to a factor of 30 ..."
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Cited by 4 (0 self)
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Abstract. In this paper we solve the optimal rectangle packing problem using Cumulative and Disjoint2 constraints in SICStus Prolog with a novel decomposition method, together with a specialized search routine and various model enhancements. We improve the best known runtimes by up to a factor
On Approximating Rectangle Tiling and Packing
 Proc Symp. on Discrete Algorithms (SODA
"... Our study of tiling and packing with rectangles in twodimensional regions is strongly motivated by applications in database mining, histogrambased estimation of query sizes, data partitioning, and motion estimation in video compression by block matching, among others. An example of the problems tha ..."
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Cited by 47 (6 self)
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Our study of tiling and packing with rectangles in twodimensional regions is strongly motivated by applications in database mining, histogrambased estimation of query sizes, data partitioning, and motion estimation in video compression by block matching, among others. An example of the problems
Optimal rectangle packing: Initial results
 In Proceedings of the 13th International Conference on Automated Planning and Scheduling (ICAPS2003
"... Given a set of rectangles with fixed orientations, we want to find an enclosing rectangle of minimum area that contains them all with no overlap. Many simple scheduling tasks can be modelled by this NPcomplete problem. We use an anytime branchandbound algorithm to solve the problem optimally. Our ..."
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Cited by 19 (5 self)
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squarepacking problems as a simple and easilyspecified benchmark. The squarepacking problem of size N is to find the smallest rectangle that contains the 1x1, 2x2, etc. up to NxN square. We find optimal solutions to
Optimal Rectangle Packing: New Results
, 2004
"... We present new results on the problem of finding an enclosing rectangle of minimum area that will contain a given a set of rectangles. Many simple scheduling tasks can be modelled by this NPcomplete problem. We present a new lower bound on the amount of wasted space in a partial solution, a new dom ..."
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Cited by 18 (1 self)
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We present new results on the problem of finding an enclosing rectangle of minimum area that will contain a given a set of rectangles. Many simple scheduling tasks can be modelled by this NPcomplete problem. We present a new lower bound on the amount of wasted space in a partial solution, a new
New Improvements in Optimal Rectangle Packing
"... The rectangle packing problem consists of finding an enclosing rectangle of smallest area that can contain a given set of rectangles without overlap. Our algorithm picks the xcoordinates of all the rectangles before picking any of the ycoordinates. For the xcoordinates, we present a dynamic varia ..."
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Cited by 4 (2 self)
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The rectangle packing problem consists of finding an enclosing rectangle of smallest area that can contain a given set of rectangles without overlap. Our algorithm picks the xcoordinates of all the rectangles before picking any of the ycoordinates. For the xcoordinates, we present a dynamic
Optimal packing of highprecision rectangles
 In
, 2011
"... The rectanglepacking problem consists of finding an enclosing rectangle of smallest area that can contain a given set of rectangles without overlap. Our new benchmark includes rectangles of successively higher precision, a problem for the previous stateoftheart, which enumerates all locations fo ..."
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Cited by 1 (1 self)
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The rectanglepacking problem consists of finding an enclosing rectangle of smallest area that can contain a given set of rectangles without overlap. Our new benchmark includes rectangles of successively higher precision, a problem for the previous stateoftheart, which enumerates all locations
Equivalence and Dominance for Problems of Optimal Packing of Rectangles
, 1995
"... In this paper we consider the problem of optimal packing of small rectangles within a larger rectangle. The topic consists of a comprehensive investigation of equivalence and dominance of packing patterns. Using suitable kinds of equivalence and dominance, the goal is to develop an efficient branch& ..."
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Cited by 7 (3 self)
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In this paper we consider the problem of optimal packing of small rectangles within a larger rectangle. The topic consists of a comprehensive investigation of equivalence and dominance of packing patterns. Using suitable kinds of equivalence and dominance, the goal is to develop an efficient branch
VLSI module placement based on rectanglepacking by the sequence pair
 IEEE TRANS. ON CAD
, 1996
"... The earliest and the most critical stage in VLSI layout design is the placement. The background of which is the rectangle packing problem: Given set of rectangular modules of arbitrary sizes, place them without overlap on a plane within a rectangle of minimum area. Since the variety of the packing ..."
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Cited by 131 (7 self)
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The earliest and the most critical stage in VLSI layout design is the placement. The background of which is the rectangle packing problem: Given set of rectangular modules of arbitrary sizes, place them without overlap on a plane within a rectangle of minimum area. Since the variety of the packing
The R+tree: A dynamic index for multidimensional objects
 PROC. 13TH VLDB CONF
, 1987
"... The problem of indexing multidimensional objects is considered. First, a classification of existing methods is given along with a discussion of the major issues involved in multidimensional data indexing. Second, a variation to Guttman’s Rtrees (R +trees) that avoids overlapping rectangles in inte ..."
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Cited by 345 (19 self)
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The problem of indexing multidimensional objects is considered. First, a classification of existing methods is given along with a discussion of the major issues involved in multidimensional data indexing. Second, a variation to Guttman’s Rtrees (R +trees) that avoids overlapping rectangles
Optimal rectangle packing: A metaCSP approach
, 2006
"... We present a new approach to optimal rectangle packing, an NPcomplete problem that can be used to model many simple scheduling tasks. Recent attempts at incorporating artificial intelligence search techniques to the problem of rectangle packing have focused on a CSP formulation, in which partial as ..."
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Cited by 11 (1 self)
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We present a new approach to optimal rectangle packing, an NPcomplete problem that can be used to model many simple scheduling tasks. Recent attempts at incorporating artificial intelligence search techniques to the problem of rectangle packing have focused on a CSP formulation, in which partial
Results 1  10
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