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arXiv 2405.02002cs.DC
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网格上机器人分散问题的优化:有无容错机制

Optimizing Robot Dispersion on Grids: with and without Fault Tolerance

Rik Banerjee, Manish Kumar, Anisur Rahaman Molla

AI总结:

本文研究无向网格上移动机器人的分散问题,提出三种确定性算法,在有无故障机器人情况下分别实现时间与内存最优或近最优的分散,并给出相应的复杂度上界。

摘要:

在匿名图节点上分散移动机器人的引入与研究近来受到越来越多的关注,并已在多种图类和设定中得到了探索。虽然针对有向网格已经建立了最优分散解 [Kshemkalyani 等,WALCOM 2020],但一个重要的未解决问题是:在无向网格上是否能够实现最优分散。本文研究了无向网格上的分散问题,同时考虑无故障机器人和故障机器人两种情况。无向网格带来的挑战在于,单个机器人在节点之间移动时缺乏明确的方向感,这与有向网格中直接的导航方式形成对比。我们提出了三种针对我们机器人模型的确定性算法。第一种和第二种算法分别处理有向网格和无向网格中故障机器人与无故障机器人的分散问题,并同时保证时间和内存的最优化。故障机器人随时可能发生崩溃,从而导致永久性失效。在这两种设定下,我们均在 O(√n) 轮内实现分散,且每个机器人仅需 O(log n) 比特的内存。第三种算法处理无向网格中易发生崩溃故障的机器人。在该场景下,我们的算法在 O(√n log n) 时间内运行,并且每个机器人使用 O(√n log n) 比特的内存。机器人需要知道 n 的值才能终止。

英文摘要:

The introduction and study of dispersing mobile robots across the nodes of an anonymous graph have recently gained traction and have been explored within various graph classes and settings. While optimal dispersion solution was established for {\em oriented} grids [Kshemkalyani et al., WALCOM 2020], a significant unresolved question pertains to whether achieving optimal dispersion is feasible on an {\em unoriented} grid. This paper investigates the dispersion problem on unoriented grids, considering both non-faulty and faulty robots. The challenge posed by unoriented grids lies in the absence of a clear sense of direction for a single robot moving between nodes, as opposed to the straightforward navigation of oriented grids. We present three deterministic algorithms tailored to our robot model. The first and second algorithms deal with the dispersion of faulty and non-faulty robots, ensuring both time and memory optimization in oriented and unoriented grids, respectively. Faulty robots that are prone to crashing at any time, causing permanent failure. In both settings, we achieve dispersion in $O(\sqrt{n})$ rounds while requiring $O(\log n)$ bits of memory per robot. The third algorithm tackles faulty robots prone to crash faults in an unoriented grid. In this scenario, our algorithm operates within $O(\sqrt{n} \log n)$ time and uses $O(\sqrt{n} \log n)$ bits of memory per robot. The robots need to know the value of $n$ for termination.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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