多项式步长的自稳定断开元件检测与有根最短路径树维护
Self-Stabilizing Disconnected Components Detection and Rooted Shortest-Path Tree Maintenance in Polynomial Steps
摘要：
我们处理的问题，保持最短路径树植根于一些进程r在网络中，可能会断开拓扑变化后。然后，目标是在其连接组件中维护以r为根的最短路径树，并且使其他组件的所有进程检测到r不是其连接组件的一部分。我们提出，在复合原子模型中，一个沉默的自稳定算法，这个问题的工作在半匿名网络，边缘有严格的正权重。该算法不需要任何关于网络全局参数的先验知识。我们证明了它的正确性，假设分布式不公平的守护进程，最一般的守护进程。它的循环稳定时间至多为3nmax+D，其中nmax是连通分支中非根过程的最大个数，D是Vr的跳直径.此外，如果我们另外假设边的权重是正整数，那么它在多项式步骤中稳定下来：也就是说，我们展示了O（maxi nmax^3 n）的界，其中maxi是边的最大权重，n是进程的数量。
英文摘要：
We deal with the problem of maintaining a shortest-path tree rooted at some process r in a network that may be disconnected after topological changes. The goal is then to maintain a shortest-path tree rooted at r in its connected component, V\_r, and make all processes of other components detecting that r is not part of their connected component. We propose, in the composite atomicity model, a silent self-stabilizing algorithm for this problem working in semi-anonymous networks, where edges have strictly positive weights. This algorithm does not require any a priori knowledge about global parameters of the network. We prove its correctness assuming the distributed unfair daemon, the most general daemon. Its stabilization time in rounds is at most 3nmax+D, where nmax is the maximum number of non-root processes in a connected component and D is the hop-diameter of V\_r. Furthermore, if we additionally assume that edge weights are positive integers, then it stabilizes in a polynomial number of steps: namely, we exhibit a bound in O(maxi nmax^3 n), where maxi is the maximum weight of an edge and n is the number of processes.
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。
