基于组合拓扑的轮基模型的K集一致界
K set-agreement bounds in round-based models through combinatorial topology
摘要：
基于圆形的模型是非常常见的消息传递模型;应用于分布式计算的组合拓扑提供了广泛的结果，如一般的下界。我们结合两者来研究k-集一致性的可计算性。在所有可能的基于轮的模型中，我们考虑不经意的，其中的约束是由一组允许的图每轮只轮。在不经意的模型中，我们重点关注上面闭合的模型，即可能的图集包含比某些起始图具有更多边的所有图的模型。它们直观地捕捉了某些通信模型所需的底层结构，比如包含一个环。然后，我们推导出一个回合的K-集协议的下限和上限，这些界限证明使用组合拓扑，但只在图形属性方面。当限制我们的算法时，这些界限扩展到多轮-只召回成对的进程和初始值，而不是谁发送了什么和什么时候。
英文摘要：
Round-based models are very common message-passing models; combinatorial topology applied to distributed computing provides sweeping results like general lower bounds. We combine both to study the computability of k-set agreement. Among all the possible round-based models, we consider oblivious ones, where the constraints are given only round per round by a set of allowed graphs. And among oblivious models, we focus on closed-above ones, that is models where the set of possible graphs contains all graphs with more edges than some starting graphs. These capture intuitively the underlying structure required by some communication model, like containing a ring. We then derive lower bounds and upper bounds in one round for k-set agreement, such that these bounds are proved using combinatorial topology but stated only in terms of graph properties. These bounds extend to multiple rounds when limiting our algorithms to be oblivious -- recalling only pairs of processes and initial value, not who send what and when.
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