有机器人存在时的二次曲线形成
Conic Formation in Presence of Faulty Robots
摘要：
模式形成是分布式计算中最基本的问题之一，近年来受到广泛关注。在本文中，我们开始研究分布式模式形成的情况下，一些机器人可以\textit{faulty}。特别是，我们认为建立良好的\textit{look-compute-move}模型与遗忘，匿名机器人。我们首先提出了下界，并表明，任何确定性算法至少需要两轮，以形成简单的模式存在故障的机器人。然后，我们提出了分布式算法，我们的问题，匹配这个界限，\textit{for conic sections}：在最多两轮，机器人形成线，圆圈和抛物线容忍$f=2,3$和$4$故障，分别。对于$f=5$，目标图案是抛物线、双曲线和椭圆。我们表明，由此产生的模式包括$f$故障机器人的模式中的$n$机器人，其中$n \geq 2f+1$，和$f < n < 2f+1$机器人不能形成这样的模式。最后，我们讨论几个放宽和扩展。
英文摘要：
Pattern formation is one of the most fundamental problems in distributed computing, which has recently received much attention. In this paper, we initiate the study of distributed pattern formation in situations when some robots can be \textit{faulty}. In particular, we consider the well-established \textit{look-compute-move} model with oblivious, anonymous robots. We first present lower bounds and show that any deterministic algorithm takes at least two rounds to form simple patterns in the presence of faulty robots. We then present distributed algorithms for our problem which match this bound, \textit{for conic sections}: in at most two rounds, robots form lines, circles and parabola tolerating $f=2,3$ and $4$ faults, respectively. For $f=5$, the target patterns are parabola, hyperbola and ellipse. We show that the resulting pattern includes the $f$ faulty robots in the pattern of $n$ robots, where $n \geq 2f+1$, and that $f < n < 2f+1$ robots cannot form such patterns. We conclude by discussing several relaxations and extensions.
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