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Asymptotic distributions for the cost of linear probing hashing, Random Structures and Algorithms
"... Abstract. We study moments and asymptotic distributions of the construction cost, measured as the total displacement, for hash tables using linear probing. Four different methods are employed for different ranges of the parameters; together they yield a complete description. This extends earlier res ..."
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Cited by 11 (3 self)
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Abstract. We study moments and asymptotic distributions of the construction cost, measured as the total displacement, for hash tables using linear probing. Four different methods are employed for different ranges of the parameters; together they yield a complete description. This extends earlier results by Flajolet, Poblete and Viola. The average cost of unsuccessful searches is considered too. 1.
SIMPLY GENERATED TREES, CONDITIONED GALTON–WATSON TREES, RANDOM ALLOCATIONS AND CONDENSATION (EXTENDED ABSTRACT)
, 2012
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Moment Convergence In Conditional Limit Theorems
, 2000
"... . Consider a sum P N 1 Y i of random variables conditioned on a given value of the sum P N 1 X i of some other variables, where X i and Y i are dependent but the pairs (X i ; Y i ) form an i.i.d. sequence. We prove, for a triangular array (X ni ; Y ni ) of such pairs satisfying certain condi ..."
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Cited by 5 (4 self)
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. Consider a sum P N 1 Y i of random variables conditioned on a given value of the sum P N 1 X i of some other variables, where X i and Y i are dependent but the pairs (X i ; Y i ) form an i.i.d. sequence. We prove, for a triangular array (X ni ; Y ni ) of such pairs satisfying certain conditions, both convergence of the distribution of the conditioned sum (after suitable normalization) to a normal distribution, and convergence of its moments. The results are motivated by an application to hashing with linear probing; we give also some other applications to occupancy problems, random forests, and branching processes. 1. Introduction Many random variables arising in different areas of probability theory, combinatorics and statistics turn out to have the same distribution as a sum of independent random variables conditioned on a specific value of another such sum. More precisely, we are concerned with variables with the distribution of P N 1 Y i conditioned on P N 1 X...
Individual displacements for linear probing hashing with different insertion policies
 ACM Transactions on Algorithms
, 2005
"... Abstract. We study the distribution of the individual displacements in hashing with linear probing for three different versions: First Come, Last Come and Robin Hood. Asymptotic distributions and their moments are found when the the size of the hash table tends to infinity with the proportion of occ ..."
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Cited by 4 (1 self)
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Abstract. We study the distribution of the individual displacements in hashing with linear probing for three different versions: First Come, Last Come and Robin Hood. Asymptotic distributions and their moments are found when the the size of the hash table tends to infinity with the proportion of occupied cells converging to some α, 0 < α < 1. (In the case of Last Come, the results are more complicated and less complete than in the other cases.) We also show, using the diagonal Poisson transform studied by Poblete, Viola and Munro, that exact expressions for finite m and n can be obtained from the limits as m, n → ∞. We end with some results, conjectures and questions about the shape of the limit distributions. These have some relevance for computer applications. 1.
ON THE SPREAD OF RANDOM GRAPHS
"... Abstract. The spread of a connected graph G was introduced by Alon, Boppana and Spencer [1] and measures how tightly connected the graph is. It is defined as the maximum over all Lipschitz functions f on V (G) of the variance of f(X) when X is uniformly distributed on V (G). We investigate the sprea ..."
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Abstract. The spread of a connected graph G was introduced by Alon, Boppana and Spencer [1] and measures how tightly connected the graph is. It is defined as the maximum over all Lipschitz functions f on V (G) of the variance of f(X) when X is uniformly distributed on V (G). We investigate the spread for certain models of sparse random graph; in particular for random regular graphs G(n, d), for ErdősRényi random graphs Gn,p in the supercritical range p> 1/n, and for a ‘small world’ model. For supercritical Gn,p, we show that if p = c/n with c> 1 fixed then with high probability the spread of the giant component is bounded, and we prove corresponding statements for other models of random graphs, including a model with random edgelengths. We also give lower bounds on the spread for the barely supercritical case when p = (1+o(1))/n. Further, we show that for d large, with high probability the spread of G(n, d) becomes arbitrarily close to that of the complete graph Kn. 1.