Discrete configuration spaces of squares and hexagons

Discrete configuration spaces of squares and hexagons
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正方形和六边形的离散配置空间

DOI:
10.1007/s41468-019-00043-w
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发表时间:
2020
期刊:
Journal of Applied and Computational Topology
影响因子:
--
通讯作者:
Alpert, Hannah
Alpert, Hannah
中科院分区:
--
文献类型:
--
作者:
Alpert, Hannah

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小球体占据一个大盒子的固定部分;这些球体在盒子中可用的空间内移动有多困难?这种困难如何取决于所选择的密度?我们考虑这个问题的离散版本,一个熟悉的4 × 4方形网格上的15块滑动拼图的推广。在有更多碎片和更多洞的更大网格中,我们能以多快的速度将谜题移至已解状态?我们考虑滑动方块和滑动六边形的这些问题,以模拟非常密集的磁盘。
A fixed fraction of a large box is occupied by tiny spheres; how difficult is it for those spheres to move around in the space available in the box, and how does that difficulty depend on the chosen density? We consider a discrete version of this problem, a generalization of the familiar fifteen-piece sliding puzzle on the 4 by 4 square grid. On larger grids with more pieces and more holes, asymptotically how fast can we move the puzzle into the solved state? We consider these questions for both sliding squares and sliding hexagons, to model very densely packed disks.
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