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arXiv · 2601.13047

Exploration on Highly Dynamic Graphs

Ashish Saxena·Kaushik Mondal
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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.

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Ashish Saxena, Kaushik Mondal. 2026-01-19. Exploration on Highly Dynamic Graphs. https://arxiv.org/abs/2601.13047

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