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

Abstract

Starting with a monodisperse configuration with nn size-1 particles, an additive Marcus-Lushnikov process evolves until it reaches its final state (a unique particle with mass nn). At each of the nāˆ’1n-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 kkth clustering, under various regimes for (n,k)(n,k), with applications to the study of Union--Find algorithms.Comment: 28 pages, 1 figur

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