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Hardness of Reconfiguring Robot Swarms with Uniform External Control in Limited Directions
arXiv - CS - Emerging Technologies Pub Date : 2020-03-29 , DOI: arxiv-2003.13097
David Caballero, Angel A. Cantu, Timothy Gomez, Austin Luchsinger, Robert Schweller, Tim Wylie

Motivated by advances is nanoscale applications and simplistic robot agents, we look at problems based on using a global signal to move all agents when given a limited number of directional signals and immovable geometry. We study a model where unit square particles move within a 2D grid based on uniform external forces. Movement is based on a sequence of uniform commands which cause all particles to move 1 step in a specific direction. The 2D grid board additionally contains "blocked" spaces which prevent particles from entry. Within this model, we investigate the complexity of deciding 1) whether a target location on the board can be occupied (by any) particle (\emph{occupancy problem}), 2) whether a specific particle can be relocated to another specific position in the board (\emph{relocation problem}), and 3) whether a board configuration can be transformed into another configuration (\emph{reconfiguration problem}). We prove that while occupancy is solvable in polynomial time, the relocation and reconfiguration problems are both NP-Complete even when restricted to only 2 or 3 movement directions. We further define a hierarchy of board geometries and show that this hardness holds for even very restricted classes of board geometry.

中文翻译:

在有限方向上使用统一外部控制重新配置机器人群的硬度

受到纳米级应用和简单机器人代理的推动,当给定有限数量的方向信号和不可移动的几何形状时,我们研究基于使用全局信号移动所有代理的问题。我们研究了一个模型,其中单位正方形粒子基于均匀的外力在 2D 网格内移动。运动基于一系列统一命令,这些命令使所有粒子向特定方向移动 1 步。2D 网格板还包含“阻塞”空间,可防止粒子进入。在这个模型中,我们研究了决定 1) 板上的目标位置是否可以被(任何)粒子占据(\emph{occupancy problem}),2)是否可以将特定粒子重新定位到另一个特定位置的复杂性董事会(\emph{搬迁问题}),和 3) 电路板配置是否可以转换为另一种配置(\emph{reconfiguration problem})。我们证明,虽然占用率可以在多项式时间内解决,但即使仅限于 2 或 3 个移动方向,重定位和重新配置问题也是 NP-Complete 问题。我们进一步定义了棋盘几何的层次结构,并表明这种硬度甚至适用于非常有限的棋盘几何等级。
更新日期:2020-03-31
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