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On two dimensional packing [chapter]

Yossi Azar, Leah Epstein
1996 Lecture Notes in Computer Science  
The paper considers packing of rectangles into an in nite bin. Similar to the Tetris game, the rectangles arrive from the top and, once placed, cannot be moved again.  ...  In contrast, if rotations are not allowed, we show that no algorithm of constant ratio exists.  ...  In the original two-dimensional packing problem, a rectangle could be placed directly in any free space of the size of the rectangle, the concept of getting into a place was not discussed.  ... 
doi:10.1007/3-540-61422-2_142 fatcat:qs7z75qlhvhrtfaqcyo22okr5i

On Two Dimensional Packing

Yossi Azar, Leah Epstein
1997 Journal of Algorithms  
The paper considers packing of rectangles into an in nite bin. Similar to the Tetris game, the rectangles arrive from the top and, once placed, cannot be moved again.  ...  In contrast, if rotations are not allowed, we show that no algorithm of constant ratio exists.  ...  In the original two-dimensional packing problem, a rectangle could be placed directly in any free space of the size of the rectangle, the concept of getting into a place was not discussed.  ... 
doi:10.1006/jagm.1997.0876 fatcat:dps2ww2bgrfsxm7fid5ak5l3by

Volvox barberi flocks, forming near-optimal, two-dimensional, polydisperse lattice packings [article]

Ravi Nicholas Balasubramanian
2018 arXiv   pre-print
A dye tracer in the Volvox medium revealed large hydrodynamic vortices generated by colony and flock rotations, providing a likely source of the forces leading to flocking and optimal packing.  ...  The colonies in flocks form two-dimensional, irregular, "active crystals", with lattice angles and colony diameters both following log-normal distributions.  ...  colonies gather into packed two-dimensional lattices over a period of minutes.  ... 
arXiv:1803.03542v2 fatcat:x4ziojy3infjhgwisdm4xhnjfy

Two-dimensional packing in prolate granular materials

K. Stokely, A. Diacou, Scott V. Franklin
2003 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
We investigate the two-dimensional packing of extremely prolate (aspect ratio α=L/D>10) granular materials, comparing experiments with Monte-Carlo simulations.  ...  The average packing fraction of particles with aspect ratio α=12 is 0.68±0.03. We quantify the orientational correlation of particles and find a correlation length of two particle lengths.  ...  Saul Lapidus and Peter Gee were involved in much of the original setup of the experiment.  ... 
doi:10.1103/physreve.67.051302 pmid:12786141 fatcat:ywvsaqcmorefzangzaaozgyaq4

Two-dimensional packing for irregular shaped objects

Ping Chen, Zhaohui Fu, A. Lim, B. Rodrigues
2003 36th Annual Hawaii International Conference on System Sciences, 2003. Proceedings of the  
The simplest packing problem is rectangular packing, where both the objects and the region are rectangular. Many research works have been done on two and three dimensional rectangular packing.  ...  In the project, we concentrate on two-dimensional packing problems involving irregular shaped objects (both convex and concave). We have applied several approaches to solve such problems.  ...  There are relatively few works on two dimensional packing with arbitrary shapes, compared to 2D rectangle packing. They can be classified into two types, namely nesting and packing.  ... 
doi:10.1109/hicss.2003.1174211 dblp:conf/hicss/ChenFLR03 fatcat:ekgajqxtvzgq3k7a64h7yxcesm

Two-dimensional packing problems: A survey

Andrea Lodi, Silvano Martello, Michele Monaci
2002 European Journal of Operational Research  
In two-dimensional bin packing problems these units are finite rectangles, and the objective is to pack all the items into the minimum number of units, while in two-dimensional strip packing problems there  ...  is a single standardized unit of given width, and the objective is to pack all the items within the minimum height.  ...  Acknowledgements We thank the Ministero dell'Istruzione, dell'Universit a a e della Ricerca (MIUR) and the Consiglio Nazionale delle Ricerche (CNR), Italy, for the support to the project.  ... 
doi:10.1016/s0377-2217(02)00123-6 fatcat:6trfgcr2nrgghbdr2cimh6zx4i

Volvox barberi flocks, forming near-optimal, two-dimensional, polydisperse lattice packings [article]

Ravi Balasubramanian
2018 bioRxiv   pre-print
A dye tracer in the Volvox medium revealed large hydrodynamic vortices generated by colony and flock rotations, providing a likely source of the forces leading to flocking and optimal packing.  ...  The colonies in flocks form two-dimensional, irregular, "active crystals", with lattice angles and colony diameters both following log-normal distributions.  ...  colonies gather into packed two-dimensional lattices over a period of minutes.  ... 
doi:10.1101/279059 fatcat:ltgsfw7cwrcgpabukp32qbyn4q

Vibrational properties of two-dimensional dimer packings near the jamming transition [article]

Kumpei Shiraishi, Hideyuki Mizuno, Atsushi Ikeda
2019 arXiv   pre-print
We first study the contact number of dimers near the jamming transition. It turns out that packings of dimers have "rotational rattlers", each of which still has a free rotational motion.  ...  In the present work, we study the dimer packings in two dimensions, which have been much less understood than systems of spheres and ellipsoids.  ...  This work was also partially supported by the Asahi Glass Foundation. The computations were partially performed using the Research Center for Computational Science, Okazaki, Japan.  ... 
arXiv:1905.02966v1 fatcat:scfg6we62bg3ldts332ktjgubm

Improved Approximation Algorithm for Two-Dimensional Bin Packing [chapter]

Nikhil Bansal, Arindam Khan
2013 Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms  
We study the two-dimensional bin packing problem with and without rotations.  ...  Here we are given a set of two-dimensional rectangular items I and the goal is to pack these into a minimum number of unit square bins.  ...  In this paper we consider the two dimensional bin packing problem, defined as follows.  ... 
doi:10.1137/1.9781611973402.2 dblp:conf/soda/BansalK14 fatcat:p432s7hjmnawfdlql76vptjdpu

Contact angle entropy and macroscopic friction in noncohesive two-dimensional granular packings

Juan C. Petit, Xavier García, Iván Sánchez, Ernesto Medina
2017 Physical review. E  
Molecular dynamics in two dimensions are used to simulate uniaxial loading-unloading cycles imposed on the granular packings.  ...  While macroscopic Mohr-friction depends on the granular pack geometric details, it reaches a stationary limit after a finite number of loading-unloading cycles that render well-defined values for bulk  ...  ACKNOWLEDGMENT The authors gratefully acknowledge illuminating discussions with Vanessa Urdaneta. EM acknowledges support from IVIC through the "Granular Dynamics Project" 271.  ... 
doi:10.1103/physreve.96.012902 pmid:29347060 fatcat:ipsb3w7dqzg5bovmuwdw56f4sy

Tight packing of a flexible rod in two-dimensional cavities

T A Sobral, M A F Gomes
2015 Journal of Physics D: Applied Physics  
We have performed an extensive experimental analysis of the total length L(N, X, Y) in the tight packing limit, and have obtained robust power laws relating these variables.  ...  The present work deals with the injection and packing of a flexible polymeric rod of length L into a simply connected rectangular domain of area XY.  ...  Acknowledgments We acknowledge the anonymous referees for the suggestions and critical reading of the text.  ... 
doi:10.1088/0022-3727/48/33/335305 fatcat:h6dxoivrqna3le32qbc6puqoh4

Numerical study of the stress response of two-dimensional dense granular packings

N. Gland, P. Wang, H. A. Makse
2006 The European Physical Journal E : Soft matter  
We investigate the Green function of two-dimensional dense random packings of grains in order to discriminate between the different theories of stress transmission in granular materials.  ...  We show that the agreement holds in the bulk of the packings as well as at the boundaries and we validate the linear dependence of the stress profile width with depth.  ...  This work has been supported by the Department of Energy and the National Science Foundation.  ... 
doi:10.1140/epje/i2006-10012-6 pmid:16794777 fatcat:sfacae2taze3zpfj4trimph2my

A Primal Decomposition Algorithm for the Two-dimensional Bin Packing Problem [article]

Jean-François Côté and Mohamed Haouari and Manuel Iori
2019 arXiv   pre-print
The Two-dimensional Bin Packing Problem calls for packing a set of rectangular items into a minimal set of larger rectangular bins.  ...  Items must be packed with their edges parallel to the borders of the bins, cannot be rotated and cannot overlap among them.  ...  Acknowledgments We thank Francisco Parreño for providing us with the code of Parreño et al. (2010) , David Pisinger for giving us the complete results from Pisinger and Sigurd (2007) , and Michele Monaci  ... 
arXiv:1909.06835v1 fatcat:vexf2wnasbhl7pm7nsj4h7b6qu

On Guillotine Separable Packings for the Two-dimensional Geometric Knapsack Problem [article]

Arindam Khan, Arnab Maiti, Amatya Sharma, Andreas Wiese
2021 arXiv   pre-print
In two-dimensional geometric knapsack problem, we are given a set of n axis-aligned rectangular items and an axis-aligned square-shaped knapsack.  ...  The goal is to find a (non-overlapping axis-aligned) packing of a maximum profit subset of rectangles into the knapsack.  ...  A quasi-PTAS for the two-dimensional geometric  ... 
arXiv:2103.09735v1 fatcat:yvju6fu2hbhzrjwxoq3qqkf47e

A squeaky wheel optimisation methodology for two-dimensional strip packing

Edmund K. Burke, Matthew R. Hyde, Graham Kendall
2011 Computers & Operations Research  
The two dimensional strip packing problem occurs in industries such as metal, wood, glass, paper, and textiles.  ...  The contribution of this paper is to present a much simpler but equally competitive iterative packing methodology based on squeaky wheel optimisation.  ...  This paper addresses the two dimensional orthogonal strip packing problem, where a set of rectangular shapes must be arranged onto a larger rectangle of fixed width and infinite height, while minimising  ... 
doi:10.1016/j.cor.2010.10.005 fatcat:dgsg34qipbd7ngfxk5w4yhtrwy
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