Showing papers by "Andrei Z. Broder published in 1985"

On the performance of edited nearest neighbor rules in high dimensions

Abstract: It is shown that, asymptotically, as the dimensionality of the space increases, the usual sample editing becomes independent. This makes an accurate calculation of performance in a high-dimensional space straightforward. Thus, with high dimensionality, the grouping given by J. Koplowitz and T.A. Brown (1981) is not necessary for determining the risk, and, similarly, the results presented by D.L. Wilson (1972) become very close to exact.

Two counting problems solved via string encodings

Abstract: The common feature of the two problems presented in this paper is the use of bijective string encodings to solve counting questions. The first problem deals with a “natural” object — the size of the transitive closure of a random mapping. In the second problem certain contrived combinatorial objects are counted in two different ways in order to devise a new class of Abelian identities.

A provably secure polynomial approximation scheme for the distributed lottery problem (extended abstract)

Abstract: 1. I n t r o d u c t i o n The subject of this paper is a protocol ~0r distributed lottery agreement (DLA), that is defined as agreement on an unbiased random bit in a network of n processors, out of which up to t might be faulty and malicious. The interest in this problem was sparked by the work of Rabin ([Rabin83]) who showed that in such an environment it is possible to achieve agreement on a sender's value (Byzantine agreement 1) in constant expected time, provided that at each round all processors have access to a common random bit, S e e n e x t s e c t i o n f o r d e f i n i t i o n s . Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. ©1985 ACM 0-89791-167-9/1985/0800-0136 $00.75

Weighted Random Mappings; Properties and Applications.

Abstract: : A random mapping is a random graph where ever vertex has outdegree one. Previous work was concerned mostly with a uniform probability distribution on these mappings. In contrast, this investigation assumed a non-uniform model, where differ mappings have different probabilities. An important application is the analysis of factorization heuristic due to Pollard and Brent. The model involved is a random mapping where every vertex has indegree either 0 or d. This distribution belongs to class called permutation invariant. A study of the general properties of permutation invariant mappings combined with the analysis of this particular distribution made possible the computation of the expected running time of this factorization method, settling an open conjecture of Pollard.

Weighted random mappings; properties and applications (integer factorization, pollard's rmo method)

Abstract: A random mapping is a random graph where every vertex has outdegree one. Previous work was concerned mostly with a uniform probability distribution on these mappings. In contrast, this investigation assumes a non-uniform model, where different mappings have different probabilities. An important application is the analysis of a factorization heuristic due to Pollard and Brent. The model involved is a random mapping where every vertex has indegree either 0 or d. This distribution belongs to a class called permutation invariant. A study of the general properties of permutation invariant mappings combined with the analysis of this particular distribution made possible the computation of the expected running time of this factorization method, settling an open conjecture of Pollard.