# Improved Lower Bound for Competitive Graph Exploration

arXiv: https://arxiv.org/abs/2002.10958 · HTML: https://mlsanity.com/paper/2002.10958/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2020.

## Built on by (most cited first, 2 of 2)

- [Robustification of Online Graph Exploration Methods](https://mlsanity.com/paper/2112.05422/) (2021)
- [Ariadne and Theseus: Exploration and Rendezvous with Two Mobile Agents in an Unknown Graph](https://mlsanity.com/paper/2403.07748/) (2024)

## Abstract (arXiv)

We give an improved lower bound of 10/3 on the competitive ratio for the exploration of an undirected, edge-weighted graph with a single agent that needs to return to the starting location after visiting all vertices. We assume that the agent has full knowledge of all edges incident to visited vertices, and, in particular, vertices have unique identifiers. Our bound improves a lower bound of 2.5 by Dobrev et al. [SIROCCO'12] and also holds for planar graphs, where it complements an upper bound of 16 by Kalyanasundaram and Pruhs[TCS'94]. The question whether a constant competitive ratio can be achieved in general remains open.