Exploration on Highly Dynamic Graphs

2026-01-19

AI Summary

This study investigates the exploration problem for mobile agents in highly dynamic graphs, focusing on the 1-Interval Connectivity and Connectivity Time models. Leveraging tools from distributed computing theory, graph-theoretic modeling, and impossibility analysis, the work strengthens the known impossibility result under 1-Interval Connectivity and establishes, for the first time, a tight bound in the Connectivity Time model: exploration is impossible with at most $(n-1)(n-2)/2$ agents, yet becomes feasible with $(n-1)(n-2)/2 + 1$ agents equipped with 1-hop visibility and $O(\log n)$ memory. This result significantly improves the previously known lower bound and highlights the critical role of local visibility in determining the feasibility of exploration in dynamic networks.

Technology Category

• Multiagent Systems: Other Foundations of Multi Agent Systems
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Security and Privacy: Large-scale security measurements

Abstract

We study the exploration problem by mobile agents in two prominent models of dynamic graphs: $1$-Interval Connectivity and Connectivity Time. The $1$-Interval Connectivity model was introduced by Kuhn et al.~[STOC 2010], and the Connectivity Time model was proposed by Michail et al.~[JPDC 2014]. Recently, Saxena et al.~[TCS 2025] investigated the exploration problem under both models. In this work, we first strengthen the existing impossibility results for the $1$-Interval Connectivity model. We then show that, in Connectivity Time dynamic graphs, exploration is impossible with $\frac{(n-1)(n-2)}{2}$ mobile agents, even when the agents have full knowledge of all system parameters, global communication, full visibility, and infinite memory. This significantly improves the previously known bound of $n$. Moreover, we prove that to solve exploration with $\frac{(n-1)(n-2)}{2}+1$ agents, $1$-hop visibility is necessary. Finally, we present an exploration algorithm that uses $\frac{(n-1)(n-2)}{2}+1$ agents, assuming global communication, $1$-hop visibility, and $O(\log n)$ memory per agent.

Problem

• dynamic graphs
• graph exploration
• mobile agents
• 1-Interval Connectivity
• Connectivity Time

Innovation

• Dynamic Graphs
• Mobile Agents
• Graph Exploration
• Impossibility Results
• Connectivity Time