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THE NEAREST UNVISITED VERTEX WALK ON RANDOM GRAPHS
Probability in the Engineering and Informational Sciences ( IF 1.1 ) Pub Date : 2021-04-05 , DOI: 10.1017/s0269964821000115
David J. Aldous

We revisit an old 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.



中文翻译:

随机图上最近未访问的顶点行走

我们重新审视算法中的一个老话题,有限图上的确定性行走,它总是向最近的未访问顶点移动,直到每个顶点都被访问。这个覆盖时间和球覆盖(度量熵)测量之间存在基本联系。对于一些熟悉的随机图模型,这种联系允许从第一次渗透估计中推断出覆盖时间的数量级。建立更清晰的结果似乎是一个具有挑战性的问题。

更新日期:2021-04-05
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