利用时间打破对称：普遍确定性匿名回归
Using Time to Break Symmetry: Universal Deterministic Anonymous Rendezvous
摘要：
两个匿名移动代理在匿名图中同步导航，并且必须使用确定性算法在节点处相遇。这是一个对称性破坏任务，称为会合，相当于代理之间的领导者选举的基本任务。在完全匿名的环境中，什么时候才是可行的？它是已知的，代理人总是可以满足，如果他们的初始位置是不对称的，如果他们是对称的，代理人同时开始，然后会合是不可能的。对于非同时启动的对称初始位置会发生什么？两个智能体之间的对称性是否会被它们的启动时间之间的延迟所破坏？为了回答这些问题，我们考虑{ \em时空初始组态}（简称STIC）。STIC被形式化为$[(u,v),δ]$，其中$u$和$v$是某些图中代理的初始节点，而$δ$是表示它们的开始时间之间的差的非负整数。一个STIC是{ \em可行}，如果存在一个确定性的算法，甚至专门为这个特定的STIC，它完成了会合it. We的主要结果是所有可行的STIC和设计的一个通用的确定性算法，完成会合所有的代理没有{ \em任何}的先验知识。因此，就可行性而言，我们完全解决了匿名图中两个匿名代理之间的对称性破缺问题。此外，我们表明，这样一个通用的算法不能为所有可行的STIC在时间多项式的代理之间的初始距离。
英文摘要：
Two anonymous mobile agents navigate synchronously in an anonymous graph and have to meet at a node, using a deterministic algorithm. This is a symmetry breaking task called rendezvous, equivalent to the fundamental task of leader election between the agents. When is this feasible in a completely anonymous environment? It is known that agents can always meet if their initial positions are nonsymmetric, and that if they are symmetric and agents start simultaneously then rendezvous is impossible. What happens for symmetric initial positions with non-simultaneous start? Can symmetry between the agents be broken by the delay between their starting times? In order to answer these questions, we consider {\em space-time initial configurations} (abbreviated by STIC). A STIC is formalized as $[(u,v),δ]$, where $u$ and $v$ are initial nodes of the agents in some graph and $δ$ is a non-negative integer that represents the difference between their starting times. A STIC is {\em feasible} if there exists a deterministic algorithm, even dedicated to this particular STIC, which accomplishes rendezvous for it. Our main result is a characterization of all feasible STICs and the design of a universal deterministic algorithm that accomplishes rendezvous for all of them without {\em any } a priori knowledge of the agents. Thus, as far as feasibility is concerned, we completely solve the problem of symmetry breaking between two anonymous agents in anonymous graphs. Moreover, we show that such a universal algorithm cannot work for all feasible STICs in time polynomial in the initial distance between the agents.
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