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Collaboration Without Communication: Evacuating Two Robots from a Disk

机译:没有通信的协作:从磁盘撤离两个机器人

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We consider the problem of evacuating two robots from a bounded area, through an unknown exit located on the boundary. Initially, the robots are in the center of the area and throughout the evacuation process they can only communicate with each other when they are at the same point at the same time. Having a visibility range of 0, the robots can only identify the location of the exit if they are already at the exit position. The task is to minimize the time it takes until both robots reach the exit, for a worst-case placement of the exit. For unit disks, an upper bound of 5.628 for the evacuation time is presented in [8]. Using the insight that, perhaps surprisingly, a forced meeting of the two robots as performed in the respective algorithm does not provide an exchange of any non-trivial information, we design a simpler algorithm that achieves an upper bound of 5.625. Our numerical simulations suggest that this bound is optimal for the considered natural class of algorithms. For dealing with the technical difficulties in analyzing the algorithm, we formulate a powerful new criterion that, for a given algorithm, reduces the number of possible worst-case exits radically. This criterion is of independent interest and can be applied to any area shape. Due to space restrictions, this version of the paper contains no proofs or illustrating figures; the full version can be found at http://disco.ethz.ch/publications/ciac2017-robotevac.pdf.
机译:我们考虑通过位于边界上的未知出口撤离来自有界区域的两个机器人的问题。最初,机器人位于区域的中心,并且在整个疏散过程中,它们只能在同一时间与同一点相同时彼此通信。具有0的可见度范围,如果它们已经处于出口位置,机器人只能识别出口的位置。任务是最小化在两个机器人到达出口之前所需的时间,以便出口的最坏情况放置。对于单位磁盘,[8]介绍了疏散时间的5.628的上限。使用识别可能令人惊讶的是,在各个算法中执行的两个机器人的强制会议不提供任何非琐碎信息的交换,我们设计了一种更简单的算法,该算法实现了5.625的上限。我们的数值模拟表明,对于考虑的自然算法而言,这一界限是最佳的。为了处理分析算法的技术困难,我们制定了强大的新标准,对于给定的算法,减少了可能最坏情况的最坏情况的数量。该标准是独立的兴趣,并且可以应用于任何区域形状。由于空间限制,此版本的纸张不包含证明或说明图;完整版本可以在http://disco.ethz.ch/publications/ciac2017-robotevac.pdf找到。

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