发表机构
Indian Institute of Technology Jodhpur; Birla Institute of Technology Mesra（印度海德拉巴理工学院; 比尔拉理工学院梅斯拉分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对异步匿名无记忆机器人在崩溃故障下的最优聚集问题，提出CrashTolerantWeberGathering算法，使每个机器人独立选择同一韦伯会议节点，避免依赖指定机器人，保证有限时间内聚集并最小化总曼哈顿距离。
AI 中文摘要
我们研究了在无限网格上，受崩溃故障影响的异步、匿名且无记忆移动机器人在有限指定会议节点集合上的最优聚集问题。机器人具有全局可见性和强多重性检测能力，但既不共享坐标系，也不共享手性。目标是让所有未故障机器人在一个韦伯会议节点处聚集，并最小化它们初始位置之间的总曼哈顿距离。最多可能有n-2个机器人永久崩溃，且此类崩溃与任意延迟无法区分。现有方法通常依赖一个指定机器人来打破对称性，而该机器人的崩溃可能会无限期地阻塞其余机器人。相反，我们的方法使每个机器人能够独立地从其快照中选择相同的目标，同时依赖目标的受限最短路径保持该目标为韦伯会议节点。我们证明，在强多重性检测下，从某些完全对称的配置出发，最优聚集是不可能的。对于所有其余配置，我们的算法CrashTolerantWeberGathering()选择一个唯一的共同目标，在整个执行过程中保持其最优性，并允许未故障机器人在不等待崩溃机器人的情况下继续前进，从而保证在有限时间内完成聚集。
英文摘要
We study the \textit{optimal gathering} problem over a finite set of designated \textit{meeting nodes} for \textit{asynchronous, anonymous,} and \textit{oblivious} mobile robots on an infinite grid under crash faults. The robots have global visibility and strong multiplicity detection, but share neither a coordinate system nor chirality. The objective is to gather all non-faulty robots at a \textsc{Weber Meeting Node}, minimizing the total Manhattan distance from their initial positions. Up to $n-2$ robots may crash permanently, and such crashes are indistinguishable from arbitrary delays. Existing approaches often rely on a designated robot to break symmetry, whose crash may block the remaining robots indefinitely. Instead, our approach enables every robot to independently select the same target from its snapshot, while target-dependent restricted shortest paths preserve the target as a \textsc{Weber Meeting Node}. We prove that, under strong multiplicity detection, optimal gathering is impossible from certain fully symmetric configurations. For all remaining configurations, our algorithm \textsc{CrashTolerantWeberGathering()} selects a unique common target, preserves its optimality throughout the execution, and allows non-faulty robots to progress without waiting for crashed robots, thereby guaranteeing gathering in finite time.
