贪婪自组织的拓扑方面

F. Ahmed, O. Tirkkonen
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引用次数: 6

摘要

我们考虑自组织问题,其中代理试图就配置空间变量的值达成一致。共识和同步问题属于这一类。这些问题在集中的环境中往往是微不足道的,而非微不足道的方面往往是由自组织本身的过程直接引起的。我们讨论了拓扑的原因,为什么简单的局部贪婪算法不能创建远程顺序。实值变量的贪婪同步以直接的方式工作,而贪婪相位同步却不能,其原因是拓扑的,在后者中,存在从代理的交互图到配置空间的映射中的非平凡同伦类。我们用这样的非平凡同伦类来识别高维位形空间。然而,我们发现贪婪自组织能够为任何不具有圆分量的高维构型空间创建远程秩序。
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Topological Aspects of Greedy Self-Organization
We consider self-organization problems, where agents try to agree about the value of a configuration space variable. Problems of consensus and synchronization belong to this category. These are the problems which would often be trivial to solve in a centralized setting, and non-trivial aspects are often directly induced by the process of self-organization itself. We discuss topological reasons as to why simple locally greedy algorithms are not able to create long-range order. The reason why greedy synchronization of a real-valued variable works in a straight forward manner, whereas greedy phase synchronization does not, is topological, in the latter non-trivial homotopy classes in mappings from the interaction graph of the agents to the configuration space exist. We identify higher dimensional configuration spaces with such non-trivial homotopy classes. However, we find that greedy self-organization is able to create long-range order for any higher-dimensional configuration space that does not possess circular components.
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