Merging costs for the additive Marcus-Lushnikov process, and Union-Find algorithms

Details Merging costs for the additive Marcus-Lushnikov process, and Union-Find algorithms Merging costs for the additive Marcus-Lushnikov process, and Union-Find algorithms

2004-06-05

arxiv.org/abs/math/0406094v1

Mathematics

Probability

28 pages, 1 figure

Scientific paper

Starting with a monodisperse configuration with $n$ size-1 particles, an additive Marcus-Lushnikov process evolves until it reaches its final state (a unique particle with mass $n$). At each of the $n-1$ steps of its evolution, a merging cost is incurred, that depends on the sizes of the two particles involved, and on an independent random factor. This paper deals with the asymptotic behaviour of the cumulated costs up to the $k$th clustering, under various regimes for $(n,k)$, with applications to the study of Union--Find algorithms.

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