线性迭代分布式平均算法的不变性及其在错误检测中的应用
Invariant Properties of Linear-Iterative Distributed Averaging Algorithms and Application to Error Detection
AI总结：
该研究针对分布式系统平均一致性问题，发现线性迭代分布式平均算法的节点局部不变性，并将其用于算法执行中的错误检测。
摘要：
我们研究了由一组可相互交换信息的节点组成的分布式系统中的平均一致性问题。我们聚焦于求解该问题的一类算法：每个节点维护一个状态，并通过其入邻居（即直接向其发送信息的节点）的状态的线性组合迭代更新自身状态。这类平均算法可被视为无外部驱动输入的离散时间线性时变系统，其状态矩阵为列随机矩阵。因此，这类算法具有全局不变性，即状态变量的总和在所有时刻均保持恒定。在本文中，我们报告了上述平均算法的另一项不变性。该性质是每个节点的局部性质，反映了在平均算法执行过程中，某类量的守恒性——这类量捕获了节点从其入邻居接收到的所有值，与该节点向其出邻居（即它直接发送信息的节点）发送的所有值的总和。我们展示了如何利用这一新发现的不变量在执行平均算法时检测错误。
英文摘要：
We consider the problem of average consensus in a distributed system comprising a set of nodes that can exchange information among themselves. We focus on a class of algorithms for solving such a problem whereby each node maintains a state and updates it iteratively as a linear combination of the states maintained by its in-neighbors, i.e., nodes from which it receives information directly. Averaging algorithms within this class can be thought of as discrete-time linear time-varying systems without external driving inputs and whose state matrix is column stochastic. As a result, the algorithms exhibit a global invariance property in that the sum of the state variables remains constant at all times. In this paper, we report on another invariance property for the aforementioned class of averaging algorithms. This property is local to each node and reflects the conservation of certain quantities capturing an aggregate of all the values received by a node from its in-neighbors and all the values sent by said node to its out-neighbors (i.e., nodes to which it sends information directly) throughout the execution of the averaging algorithm. We show how this newly-discovered invariant can be leveraged for detecting errors while executing the averaging algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
