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- W1918785890 abstract "Consider the complete graph on $n$ vertices, with edge weights drawn independently from the exponential distribution with unit mean. Janson showed that the typical distance between two vertices scales as $log{n}/n$, whereas the diameter (maximum distance between any two vertices) scales as $3log{n}/n$. Bollob'{a}s et al. showed that, for any fixed k, the weight of the Steiner tree connecting $k$ typical vertices scales as $(k-1)log{n}/n$, which recovers Janson's result for $k=2$. We extend this result to show that the worst case $k$-Steiner tree, over all choices of $k$ vertices, has weight scaling as $(2k-1)log{n}/n$ and finally, we generalise this result to Steiner trees with a mixture of typical and worst case vertices." @default.
- W1918785890 created "2016-06-24" @default.
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- W1918785890 date "2015-07-15" @default.
- W1918785890 modified "2023-09-27" @default.
- W1918785890 title "Maximal Steiner Trees in the Stochastic Mean-Field Model of Distance" @default.
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- W1918785890 doi "https://doi.org/10.48550/arxiv.1507.04282" @default.
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