本文提出并研究了团 gossip 协议框架。作为完全子网络，团在各种社会、计算机和工程网络中普遍存在。通过团 gossiping，节点沿团序列进行交互。团-gossip 协议定义为任意线性节点交互，其中节点状态是线性动态系统演化的向量。当节点状态为标量并遵循平均规则时，此类协议成为团-gossip 平均算法。我们扩展了经典线图的概念，以捕捉由底层网络和特定团序列诱导的节点交互结构。我们证明了周期性团 gossip 协议的基本特征值不变性原理，这表明任何团序列的排列在通用状态转移的谱中都相同，当广义线图不含环时。我们还证明，对于具有 n 个节点的网络，可以通过 n 的因数确定的较小大小的团总是可以构造，从而导致有限时间收敛的团 gossip 平均算法，前提是 n 不是质数。特别地，当使用大小为 m 的团时，有限时间收敛可以实现当且仅当 n 能被 m 整除且它们有相同的质因数。我们为使用大小为 m 的团的团 gossiping 构造了已证明的最快有限时间收敛的团 gossip 算法。此外，通过数值示例展示了团 gossiping 的加速效果。
英文摘要：
This paper proposes and investigates a framework for clique gossip protocols. As complete subnetworks, the existence of cliques is ubiquitous in various social, computer, and engineering networks. By clique gossiping, nodes interact with each other along a sequence of cliques. Clique-gossip protocols are defined as arbitrary linear node interactions where node states are vectors evolving as linear dynamical systems. Such protocols become clique-gossip averaging algorithms when node states are scalars under averaging rules. We generalize the classical notion of line graph to capture the essential node interaction structure induced by both the underlying network and the specific clique sequence. We prove a fundamental eigenvalue invariance principle for periodic clique-gossip protocols, which implies that any permutation of the clique sequence leads to the same spectrum for the overall state transition when the generalized line graph contains no cycle. We also prove that for a network with $n$ nodes, cliques with smaller sizes determined by factors of $n$ can always be constructed leading to finite-time convergent clique-gossip averaging algorithms, provided $n$ is not a prime number. Particularly, such finite-time convergence can be achieved with cliques of equal size $m$ if and only if $n$ is divisible by $m$ and they have exactly the same prime factors. A proven fastest finite-time convergent clique-gossip algorithm is constructed for clique-gossiping using size-$m$ cliques. Additionally, the acceleration effects of clique-gossiping are illustrated via numerical examples.
Faster Gossiping in Bidirectional Radio Networks with Large Labels
我们考虑未知的ad-hoc无线电网络，当底层网络是双向的，节点可以有多项式大标签。对于这个模型，我们提出了一个确定性的协议八卦，需要$O(n \lg^2 n \lg \lg n)$轮。这改进了[Gasienec，Potapov，Pagourtizis，Deterministic Gossiping in Radio Networks with Large labels，ESA（2002）]针对该模型的确定性流言的先前最佳结果，Gasienec，Potapov，Pagourtizis提出了针对该问题的轮复杂度$O(n \lg^3 n \lg \lg n)$的协议。这解决了在[Gasienec，Efficient gossiping in radio networks，SIROCCO（2009）]中提出的开放问题，该问题引用了该问题的下限和上限之间的桥接间隙作为重要目标。我们强调，我们的协议的一个显着特点是它的简单性，特别是相对于以前最知名的协议，这个问题。
