可达性约束下的时间网络重构
Reconfiguration of Temporal Networks under Reachability Constraints
AI总结：
该研究针对受时间可达性约束的有向时间图重构问题，证明其单源时多项式可解、双源时PSPACE难，且无环或近竞赛图的静态图中所有有效标签可相互重构，给出了多项式时间构造性算法。
AI中文摘要：
时间网络用于建模动态系统，其中边代表交互，标签指定这些交互发生的时间，示例包括交通网络、时间敏感通信网络和工业控制系统。在许多此类应用中，必须通过一系列原子修改将现有时间网络转换为期望的网络，同时在整个转换过程中保持基本功能。我们将时间标签重构问题形式化，并提供用于推理此类转换过程的理论框架。由于时间可达性是许多时间网络的核心功能，我们研究受时间可达性约束的有向时间图上的重构问题：给定带有指定源节点集的静态图，以及两个分别指示每条边可用时间的标签函数，目标是通过每次更改一条边的标签，同时始终保持源节点的时间可达性，将一个标签转换为另一个标签。我们的结果揭示了一个明显的复杂度转变：该问题在单个源节点时可在多项式时间内求解，但在两个源节点时变为PSPACE难问题。我们还证明，若静态图是无环图或近竞赛图，则所有有效标签都可相互重构。我们的证明具有构造性，可得出多项式时间算法。
英文摘要：
Temporal networks model dynamic systems in which edges represent interactions and labels specify when these interactions occur. Examples include transportation networks, time-sensitive communication networks, and industrial control systems. In many such applications, an existing temporal network must be transformed into a desired one through a sequence of atomic modifications while maintaining essential functionality throughout the transformation. We formalize the time label reconfiguration problem and provide a theoretical framework for reasoning about such transformation processes. As temporal reachability is a central functionality in many temporal networks, we study a reconfiguration problem on directed temporal graphs subject to temporal reachability constraints. We are given a static graph with a designated set of sources, along with two labeling functions indicating an availability time for every edge. The goal is to transform one labeling into the other by changing the label of a single edge at a time while maintaining temporal reachability of the sources throughout. Our results reveal a sharp complexity transition: the problem is polynomial-time solvable for a single source but becomes PSPACE-hard with two sources. We also show that if the static graph is acyclic or an almost-tournament graph, then all valid labelings can be reconfigured into each other. Our proofs are constructive and yield polynomial-time algorithms.
