Exploration on Highly Dynamic Graphs
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909994655416320 |
|---|---|
| author | Saxena, Ashish Mondal, Kaushik |
| author_facet | Saxena, Ashish Mondal, Kaushik |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13047 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exploration on Highly Dynamic Graphs Saxena, Ashish Mondal, Kaushik Distributed, Parallel, and Cluster Computing 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. |
| title | Exploration on Highly Dynamic Graphs |
| topic | Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2601.13047 |