Xheal：使用扩展器的本地化自我修复
Xheal: Localized Self-healing using Expanders
摘要：
我们考虑的问题，在可重构网络（例如对等和无线网状网络），是在反复攻击的一个无所不知的对手，并提出了一个完全分布式的算法，Xheal，保持良好的扩展和频谱特性的网络，也保持网络连接的自愈。此外，Xheal在这样做的同时只允许每个节点的低拉伸和度增加。因此，该算法修复全局属性，同时仅进行局部更改并仅使用局部信息。我们的工作改进了自修复算法“原谅树”[PODC 2008]和“原谅图”[PODC 2009]（使用类似的模型），因为我们能够保证度和拉伸，同时保持网络的扩展和频谱特性。这些修复在以下意义上保持不变量。在算法的任何一点上，图的扩展都将比只考虑对抗性插入（而不是对抗性删除）形成的图的扩展“更好”，或者扩展至少是一个常数。而且，拉伸，即愈合图中的任何节点对之间的距离不超过$O(\log n)$因子。类似地，在任何点处，对于小参数$κ$，节点$v$在仅具有对抗插入的图中的度将是$d$，在实际图中将具有至多$O(κd)$的度。我们还提供了第二个最小的特征值的拉普拉斯算子，它捕获的关键属性，如混合时间，电导，拥塞路由等我们的分布式数据结构具有低摊销延迟和带宽要求的界限。
英文摘要：
We consider the problem of self-healing in reconfigurable networks (e.g. peer-to-peer and wireless mesh networks) that are under repeated attack by an omniscient adversary and propose a fully distributed algorithm, Xheal that maintains good expansion and spectral properties of the network, also keeping the network connected. Moreover, Xheal does this while allowing only low stretch and degree increase per node. Thus, the algorithm heals global properties while only doing local changes and using only local information. Our work improves over the self-healing algorithms 'Forgiving tree'[PODC 2008] and 'Forgiving graph'[PODC 2009] (using a similar model) in that we are able to give guarantees on degree and stretch, while at the same time preserving the expansion and spectral properties of the network. These repairs preserve the invariants in the following sense. At any point in the algorithm, the expansion of the graph will be either `better' than the expansion of the graph formed by considering only the adversarial insertions (not the adversarial deletions) or the expansion will be, at least, a constant. Also, the stretch i.e. the distance between any pair of nodes in the healed graph is no more than a $O(\log n)$ factor. Similarly, at any point, a node $v$ whose degree would have been $d$ in the graph with adversarial insertions only, will have degree at most $O(κd)$ in the actual graph, for a small parameter $κ$. We also provide bounds on the second smallest eigenvalue of the Laplacian which captures key properties such as mixing time, conductance, congestion in routing etc. Our distributed data structure has low amortized latency and bandwidth requirements.
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。
