The Nearest Unvisited Vertex Walk on Random Graphs
Probability
2021-03-19 v2
Abstract
We revisit an old minor topic in algorithms, the deterministic walk on a finite graph which always moves toward the nearest unvisited vertex until every vertex is visited. There is an elementary connection between this cover time and ball-covering (metric entropy) measures. For some familiar models of random graphs, this connection allows the order of magnitude of the cover time to be deduced from first passage percolation estimates. Establishing sharper results seems a challenging problem.
Cite
@article{arxiv.1912.13175,
title = {The Nearest Unvisited Vertex Walk on Random Graphs},
author = {David Aldous},
journal= {arXiv preprint arXiv:1912.13175},
year = {2021}
}
Comments
Minor revision of original. Accepted in PEIS (Probability in the Engineering and Informational Sciences)