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Pré-Publication, Document De Travail Année : 2004

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

Philippe Chassaing
Régine Marchand

Résumé

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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Dates et versions

hal-00001664 , version 1 (05-06-2004)

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Philippe Chassaing, Régine Marchand. Merging costs for the additive Marcus-Lushnikov process, and Union-Find algorithms. 2004. ⟨hal-00001664⟩
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