Results 1 - 10 of 1,299

Using global constraints for rectangle packing

by Helmut Simonis - 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 ..."
Abstract - Cited by 4 (0 self) - Add to MetaCart
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

by Sanjeev Khanna, S. Muthukrishnan, Mike Paterson - 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, histogram-based estimation of query sizes, data partitioning, and motion estimation in video compression by block matching, among others. An example of the problems tha ..."
Abstract - Cited by 47 (6 self) - Add to MetaCart
Our study of tiling and packing with rectangles in twodimensional regions is strongly motivated by applications in database mining, histogram-based 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

by Richard E. Korf - In Proceedings of the 13th International Conference on Automated Planning and Scheduling (ICAPS-2003
"... 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 NP-complete problem. We use an anytime branch-and-bound algorithm to solve the problem optimally. Our ..."
Abstract - Cited by 19 (5 self) - Add to MetaCart
square-packing problems as a simple and easily-specified benchmark. The square-packing 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

by Richard E. Korf , 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 NP-complete problem. We present a new lower bound on the amount of wasted space in a partial solution, a new dom ..."
Abstract - Cited by 18 (1 self) - Add to MetaCart
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 NP-complete 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

by Eric Huang, Richard E. Korf
"... 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 x-coordinates of all the rectangles before picking any of the y-coordinates. For the x-coordinates, we present a dynamic varia ..."
Abstract - Cited by 4 (2 self) - Add to MetaCart
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 x-coordinates of all the rectangles before picking any of the y-coordinates. For the x-coordinates, we present a dynamic

Optimal packing of high-precision rectangles

by Eric Huang, Richard E. Korf - In , 2011
"... The rectangle-packing 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 state-of-the-art, which enumerates all locations fo ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
The rectangle-packing 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 state-of-the-art, which enumerates all locations

Equivalence and Dominance for Problems of Optimal Packing of Rectangles

by Guntram Scheithauer , 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& ..."
Abstract - Cited by 7 (3 self) - Add to MetaCart
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 rectangle-packing by the sequence pair

by Hiroshi Murata, Kunihiro Fujiyoshi, Shigetoshi Nakatake, Yoji Kajitani - 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 ..."
Abstract - Cited by 131 (7 self) - Add to MetaCart
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 multi-dimensional objects

by Timos Sellis, Nick Roussopoulos, Christos Faloutsos - 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 R-trees (R +-trees) that avoids overlapping rectangles in inte ..."
Abstract - Cited by 345 (19 self) - Add to MetaCart
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 R-trees (R +-trees) that avoids overlapping rectangles

Optimal rectangle packing: A meta-CSP approach

by Michael D. Moffitt, Martha E. Pollack , 2006
"... We present a new approach to optimal rectangle packing, an NP-complete 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 ..."
Abstract - Cited by 11 (1 self) - Add to MetaCart
We present a new approach to optimal rectangle packing, an NP-complete 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 of 1,299