Population stability：在存在对手的情况下调节大小
Population stability: regulating size in the presence of an adversary
摘要：
我们在分布式计算中引入了一个新的协调问题，我们称之为种群稳定性问题。一个系统的代理人，每个有限的内存和通信，以及复制和自毁的能力，受到攻击的最坏情况下的对手，可以在一个有界的速率（1）删除代理人任意选择和（2）插入额外的代理人与任意的初始状态到系统中。目标是永久保持种群规模在目标规模$N$的恒定因子内。这个问题的灵感来自于复杂的生物系统的能力，该系统由大量记忆有限的个体细胞组成，以在不利的环境中保持稳定的群体大小。这种生物学机制允许生物体在创伤后愈合或从炎症、疾病或正常发育引起的过度细胞增殖中恢复。我们提出了一个人口稳定性协议的通信模型，这是一个同步的变化的人口模型的Angluin等人。在每一轮中，对代理随机选择满足和交换消息，其中至少有一个恒定的分数的代理在每一轮匹配。我们的协议使用三位消息和$ω(\log^2 N)$状态每个代理。我们强调，我们的协议可以处理的对手，可以插入和删除代理，现有的近似计数技术似乎不适用的设置。该协议依赖于一种新的着色策略，其中的人口规模编码的颜色分布的方差。个体智能体可以通过从分布中采样来局部地获得种群规模的弱估计，并做出个体决策，以稳健地维持稳定的全局种群规模。
英文摘要：
We introduce a new coordination problem in distributed computing that we call the population stability problem. A system of agents each with limited memory and communication, as well as the ability to replicate and self-destruct, is subjected to attacks by a worst-case adversary that can at a bounded rate (1) delete agents chosen arbitrarily and (2) insert additional agents with arbitrary initial state into the system. The goal is perpetually to maintain a population whose size is within a constant factor of the target size $N$. The problem is inspired by the ability of complex biological systems composed of a multitude of memory-limited individual cells to maintain a stable population size in an adverse environment. Such biological mechanisms allow organisms to heal after trauma or to recover from excessive cell proliferation caused by inflammation, disease, or normal development. We present a population stability protocol in a communication model that is a synchronous variant of the population model of Angluin et al. In each round, pairs of agents selected at random meet and exchange messages, where at least a constant fraction of agents is matched in each round. Our protocol uses three-bit messages and $ω(\log^2 N)$ states per agent. We emphasize that our protocol can handle an adversary that can both insert and delete agents, a setting in which existing approximate counting techniques do not seem to apply. The protocol relies on a novel coloring strategy in which the population size is encoded in the variance of the distribution of colors. Individual agents can locally obtain a weak estimate of the population size by sampling from the distribution, and make individual decisions that robustly maintain a stable global population size.
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