The Adaptive sampling revisited

• Published in: Discrete Mathematics and Theoretical Computer Science Vol. 21 no. 3; no. Analysis of Algorithms; pp. COV1 - 27
• Main Authors: Drescher, Matthew, Louchard, Guy, Swan, Yvik
• Format: Journal Article Web Resource
• Language: English
• Published: Nancy DMTCS 01.07.2019; Maison de l'informatique et des mathematiques discretes; Discrete Mathematics & Theoretical Computer Science
• Subjects: 2010 mathematics subject classification: 68r05, 68w40; [info]computer science [cs]; Adaptive algorithms; Adaptive sampling; Algorithms; asymmetric adaptive sampling; cache; colored keys; Computer Science; Distribution functions; Hashing functions; key multiplicity; Mathematical research; Mathematics; Mathématiques; moments; periodic components; Physical, chemical, mathematical & earth Sciences; Physique, chimie, mathématiques & sciences de la terre; Random variables; Sampling (Statistics); stein method; urn model; Belgium; cache; moments; urn model; Adaptive sampling; periodic components; hashing functions; colored keys; key multiplicity; Stein method; asymmetric adaptive sampling
• ISSN: 1365-8050; 1462-7264; 1365-8050
• DOI: 10.23638/DMTCS-21-3-13

The problem of estimating the number n of distinct keys of a large collection of N data is well known in computer science. A classical algorithm is the adaptive sampling (AS). n can be estimated by R2 J , where R is the final bucket size and J is the final depth at the end of the process. Several new interesting questions can be asked about AS (some of them were suggested by P.Flajolet and popularized by J.Lumbroso). The distribution of W = log(R2 J /n) is known, we rederive this distribution in a simpler way. We provide new results on the moments of J and W. We also analyze the final cache size R distribution. We consider colored keys: assume also that among the n distinct keys, m do have color K We show how to estimate p = m n. We study keys with some multiplicity : we provide a way to estimate the total number M of some color K keys among the total number N of keys. We consider the case where we know a priori the multiplicities but not the colors. There we want to estimate the total number of keys N. An appendix is devoted to the case where the hashing function provides bits with probability different from 1/2.