par Chassaing, Philippe;Louchard, Guy 
Référence Random structures & algorithms, 21, 1, page (76-119)
Publication Publié, 2002-08
Référence Random structures & algorithms, 21, 1, page (76-119)
Publication Publié, 2002-08
Article révisé par les pairs
| Résumé : | In this paper, we consider hashing with linear probing for a hashing table with m places, n items (n < m), and ℓ = m - n empty places. For a noncomputer science-minded reader, we shall use the metaphore of n cars parking on m places: each car ci, chooses a place pi at random, and if pi is occupied, ci tries successively p i + 1, pi + 2, until it finds an empty place. Pittel proves that when ℓ/m goes to some positive limit β < 1, the size B1m, ℓ of the largest block of consecutive cars satisfies 2(β - 1 - log β) B1m, ℓ = 2 log m - 3 log log m + Ξm, where Ξm converges weakly to an extreme-value distribution. In this paper we examine at which level for n a phase transition occurs between B1m,l = o(m) and m - B1m,l = o(m). The intermediate case reveals an interesting behavior of sizes of blocks, related to the standard additive coalescent in the same way as the sizes of connected components of the random graph are related to the multiplicative coalescent. © 2002 Wiley Periodicals, Inc. |
