We consider the problem of fault-tolerant parallel search on an infinite line by n robots. Starting from the origin, the robots are required to find a target at an unknown location. The robots can move with maximum speed 1 and can communicate wirelessly among themselves. However, among the n robots, there are f robots that exhibit byzantine faults. A faulty robot can fail to report the target even after reaching it, or it can make malicious claims about having found the target when in fact it has not. Given the presence of such faulty robots, the search for the target can only be concluded when the non-faulty robots have sufficient evidence that the target has been found. We aim to design algorithms that minimize the value of Sd(n,f), the time to find a target at a (unknown) distance d from the origin by n robots among which f are faulty. We give several different algorithms whose running time depends on the ratio f/n, the density of faulty robots, and also prove lower bounds. Our algorithms are optimal for some densities of faulty robots.

中文翻译：

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Byzantine Robots 在线搜索

我们考虑无限线上的容错并行搜索问题：n机器人。从原点开始，机器人需要在未知位置找到目标。机器人可以以最大速度移动1并且可以在它们之间进行无线通信。然而，其中n机器人，有F展出的机器人拜占庭断层. 有故障的机器人即使在到达目标后也可能无法报告目标，或者它可以恶意声称已找到目标而实际上并未找到目标。鉴于此类故障机器人的存在，只有在非故障机器人有足够证据表明已找到目标时，才能结束对目标的搜索。我们的目标是设计算法以最小化小号d(n,F)，在（未知）距离处找到目标的时间d从原产地n其中机器人F有故障。我们给出了几种不同的算法，它们的运行时间取决于比率F/n，故障机器人的密度，也证明了下界。我们的算法对于某些故障机器人密度是最优的。