DFS树的快速紧凑分布式验证和自稳定
Fast and Compact Distributed Verification and Self-Stabilization of a DFS Tree
摘要：
我们提出了分布式验证和沉默稳定的DFS（深度优先搜索）生成树的连接网络的算法。计算和维护这样的DFS树是重要的任务，例如，用于构建有效的路由方案。我们的算法以各种方式改进了以前的工作。可比较的以前的工作具有空间和时间复杂度分别为每个节点的$O(n\log Δ)$比特和$O(nD)$，其中$Δ$是节点的最高度，$n$是节点的数量，$D$是网络的直径。相比之下，我们的算法有一个空间复杂度为$O(\log n)$位每节点，这是最佳的沉默稳定生成树和运行在$O(n)$时间。此外，我们的解决方案是模块化的，因为它利用分布式验证算法作为一个独立的子任务的整体解决方案。可以将验证算法用作独立任务或另一算法中的子任务。为了证明使用模块化方法构造高效DFS算法的简单性，我们还基于我们的沉默稳定DFS树提出了一个（非沉默）自稳定DFS令牌循环算法。该令牌循环算法的复杂度与已知算法相当。
英文摘要：
We present algorithms for distributed verification and silent-stabilization of a DFS(Depth First Search) spanning tree of a connected network. Computing and maintaining such a DFS tree is an important task, e.g., for constructing efficient routing schemes. Our algorithm improves upon previous work in various ways. Comparable previous work has space and time complexities of $O(n\log Δ)$ bits per node and $O(nD)$ respectively, where $Δ$ is the highest degree of a node, $n$ is the number of nodes and $D$ is the diameter of the network. In contrast, our algorithm has a space complexity of $O(\log n)$ bits per node, which is optimal for silent-stabilizing spanning trees and runs in $O(n)$ time. In addition, our solution is modular since it utilizes the distributed verification algorithm as an independent subtask of the overall solution. It is possible to use the verification algorithm as a stand alone task or as a subtask in another algorithm. To demonstrate the simplicity of constructing efficient DFS algorithms using the modular approach, We also present a (non-sielnt) self-stabilizing DFS token circulation algorithm for general networks based on our silent-stabilizing DFS tree. The complexities of this token circulation algorithm are comparable to the known ones.
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。
