Maximal Steiner Trees in the Stochastic Mean-Field Model of Distance
Keyword(s):
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 3 log n/n. Bollobás, Gamarnik, Riordan and Sudakov 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 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 generalize this result to Steiner trees with a mixture of typical and worst case vertices.
2017 ◽
Vol 26
(6)
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pp. 797-825
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2014 ◽
Vol 2014
(1)
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pp. 13D02-0
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2011 ◽
Vol 20
(08)
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pp. 1663-1675
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2010 ◽
Vol 74
(6)
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pp. 850-853
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Keyword(s):
2010 ◽
Vol 525
(1)
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pp. 29-40
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Keyword(s):
2014 ◽
pp. 297-314
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