动态网络中渐近子空间一致性问题
Asymptotic Subspace Consensus in Dynamic Networks
AI总结：
本文研究了动态网络中渐近子空间一致性的定义、可解性条件及算法退化特性，提出了一种在弱通信假设下实现子空间一致性的方法。
摘要：
我们引入了渐近子空间一致性问题，该问题要求进程的输出收敛到一个共同的子空间，同时保持在初始向量的凸包内。这是渐近一致性问题的放宽形式，后者要求输出收敛到一个单一的点，即零维仿射子空间。我们完整地刻画了在无偏消息对手下渐近子空间一致性的可解性。特别地，我们展示了大量用于渐近一致性的算法在通信网络假设较弱的分布式系统中，能够优雅地退化为渐近子空间一致性。我们还给出了达到低于初始维度的速度的界限。
英文摘要：
We introduce the problem of asymptotic subspace consensus, which requires the outputs of processes to converge onto a common subspace while remaining inside the convex hull of initial vectors.This is a relaxation of asymptotic consensus in which outputs have to converge to a single point, i.e., a zero-dimensional affine subspace. We give a complete characterization of the solvability of asymptotic subspace consensus in oblivious message adversaries. In particular, we show that a large class of algorithms used for asymptotic consensus gracefully degrades to asymptotic subspace consensus in distributed systems with weaker assumptions on the communication network. We also present bounds on the rate by which a lower-than-initial dimension is reached.
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。
