Dispersion of Mobile Robots: The Power of Randomness
Anisur Rahaman Molla, William K. Moses
备注：
20 pages, 1 table. Accepted at TAMC 2019: Theory & Applications of Models of Computation. The final authenticated version is available online at https://doi.org/10.1007/978-3-030-14812-6_30
We consider cooperation among insects, modeled as cooperation between mobile robots on a graph. Within this setting, we consider the problem of mobile robot dispersion on graphs. The study of mobile robots on a graph is an interesting paradigm with many interesting problems and applications. The problem of dispersion in this context, introduced by Augustine and Moses Jr., asks that $n$ robots, initially placed arbitrarily on an $n$ node graph, work together to quickly reach a configuration with exactly one robot at each node. Previous work on this problem has looked at the trade-off between the time to achieve dispersion and the amount of memory required by each robot. However, the trade-off was analyzed for \textit{deterministic algorithms} and the minimum memory required to achieve dispersion was found to be $Ω(\log n)$ bits at each robot. In this paper, we show that by harnessing the power of \textit{randomness}, one can achieve dispersion with $O(\log Δ)$ bits of memory at each robot, where $Δ$ is the maximum degree of the graph. Furthermore, we show a matching lower bound of $Ω(\log Δ)$ bits for any \textit{randomized algorithm} to solve dispersion.
We further extend the problem to a general $k$-dispersion problem where $k> n$ robots need to disperse over $n$ nodes such that at most $\lceil k/n \rceil$ robots are at each node in the final configuration.
Live Exploration with Mobile Robots in a Dynamic Ring, Revisited
图探索问题需要一组移动机器人，最初被任意放置在图的节点上，协同工作来探索图，使得每个节点最终被至少一个机器人访问。探索的一个重要要求是{\em终止}条件，即，机器人必须知道探索已经完成。最近在[Di Luna et al.，ICDCS 2016]。在这篇论文中，他们提出了多种算法，以解决在涉及$2$机器人时，在具有各种保证的完全同步和半同步设置下的探索问题。他们还保证，在某些假设下，使用两个机器人探索环是不可能的。一个重要的问题是$3$机器人的存在将如何影响结果。在本文中，我们试图解决这个问题，在一个完全同步的设置，也展示了如何将我们的结果扩展到一个半同步设置。特别地，我们提出了使用$3$机器人结合以下任一项进行显式终止的探索的算法：（i）机器人的唯一ID和边缘交叉检测能力（即，两个机器人在同一轮中沿相反方向移动通过边缘可以检测到彼此），或者（ii）获得随机性。我们的确定性算法的时间复杂度是渐近最优的。我们还提供了互补的不可能性结果表明，不存在任何明确的终止算法$2$机器人。理论分析和综合仿真结果表明了该算法在动态环中的有效性。我们还提出了一种算法，以实现探索与部分终止使用$3$机器人在半同步设置。
Indian Institute of Technology Indore（印度理工学院Indore分校）；University of Illinois Chicago（伊利诺伊大学芝加哥分校）；Indian Institute of Technology Madras（印度理工学院Madras分校）；Indian Statistical Institute（印度统计研究所）；Kent State University（肯特州立大学）
Beyond the Boundary: Optimal Grid Dispersion by Spread, Reverse, and Collect
Indian Institute of Technology Dhanbad（印度技术学院丹巴德）；Indian Statistical Institute Kolkata（印度统计学院加尔各答）；Indian Institute of Technology Indore（印度技术学院印多尔）；Indian Institute of Technology Delhi（印度技术学院德里）
