The strength of gnomes lies in their coordinated action. Being small and subtle creatures themselves, the forest gnomes can form large swarms acting as one giant creature. This unusual defense strategy required a lot of skill and training as directing a swarm is not an easy task! Initially, gnomes used leader-based control algorithms, although those have proven to be vulnerable to abuse and failure. After thorough research and study, gnomes developed their own leaderless consensus algorithm based on very simple rules. It is based on local broadcast (gossip) in an open network of a known radius $r$. One of the gnomes proposes a plan which then spreads gnome to gnome. If there is agreement, all gnomes act \emph{all at once}. If there are conflicting plans (an extreme rarity), they try again. The resulting swarm reaction time is exactly the swarm round-trip time $2rt$, where $t$ is the command relay time. The algorithm is non-Byzantine; all gnomes must be sane and sober.
翻译:Gnomes的力量在于它们的协同行动。作为小而微妙的生物,森林的Gnomes本身可以形成大型的群落,作为一个巨大的生物。这种不寻常的防御战略需要大量的技能和训练来引导群落,这不是一件容易的任务。最初,Gnomes使用了以领导为基础的控制算法,尽管这些算法被证明容易被滥用和失败。经过彻底的研究,Gnomes根据非常简单的规则发展了他们自己没有领导力的协商一致算法。它基于一个已知半径为$的开放网络的当地广播(gosip)。其中有一个gnome提出一个计划,然后将Gnome传播到gnome。如果有协议,所有gnomes都同时行动起来。如果计划相互冲突(极端罕见),它们会再次尝试。因此,产生的群反应时间恰恰是温和的圆曲时间2美元,其中美元是指挥中继时间。算法是非Byzantine;所有的gnomes必须是正常和清醒的。