Reconfiguration of Temporal Networks under Reachability Constraints

2026-08-03

AI Summary

This study addresses the incremental reconfiguration of edge labels in directed temporal graphs under the constraint that temporal reachability from a specified set of source vertices must be preserved throughout the transformation. Through constructive proofs, complexity analysis, and reachability algorithms, the work reveals a sharp complexity transition governed by the number of sources: the problem is solvable in polynomial time for a single source, yet becomes PSPACE-hard with just two sources. Furthermore, it establishes that any two valid labelings are mutually reachable in acyclic graphs or near-tournament graphs. This paper thus lays a theoretical foundation for temporal network reconfiguration, delineates precise computational complexity boundaries, and provides efficient reconfiguration strategies for specific graph classes.

Abstract

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.

Problem

• temporal networks
• reconfiguration
• temporal reachability
• labeling transformation
• directed temporal graphs

Innovation

• temporal reconfiguration
• temporal reachability
• PSPACE-hardness
• constructive algorithms
• time-labeled graphs