The first cycles in an evolving graph
Discrete Mathematics
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
On Poisson–Dirichlet Limits for Random Decomposable Combinatorial Structures
Combinatorics, Probability and Computing
Reflected Brownian Bridge area conditioned on its local time at the origin
Journal of Algorithms - Analysis of algorithms
Random covering of an interval and a variation of Kingman's coalescent
Random Structures & Algorithms
Individual displacements for linear probing hashing with different insertion policies
ACM Transactions on Algorithms (TALG)
| Hi-index | 0.00 |
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 pi + 1, pi + 2, until it finds an empty place. Pittel [42] proves that when ℓ/m goes to some positive limit β 1, the size B1m,ℓ1 of the largest block of consecutive cars satisfies 2(β - 1 - log β)B1m,ℓ - 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.