RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Diskr. Mat.: Year: Volume: Issue: Page: Find

 Diskr. Mat., 2018, Volume 30, Issue 2, Pages 27–36 (Mi dm1521)

Estimates of the mean size of the subset image under composition of random mappings

A. M. Zubkov, A. A. Serov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Let $\mathcal{X}_N$ be a set of $N$ elements and $F_1,F_2,\ldots$ be a sequence of random independent equiprobable mappings $\mathcal{X}_N\to\mathcal{X}_N$. For a subset $S_0\subset\mathcal{X}_N$, $|S_0|=m$, we consider a sequence of its images $S_t=F_t(\ldots F_2(F_1(S_0))\ldots)$, $t=1,2\ldots$ An approach to the exact recurrent computation of distribution of $|S_t|$ is described. Two-sided inequalities for $\mathbf{M}\{|S_t| | |S_0|=m\}$ such that the difference between the upper and lower bounds is $o(m)$ for $m,t,N\to\infty, mt=o(N)$ are derived. The results are of interest for the analysis of time-memory tradeoff algorithms.

Keywords: compositions of random mappings, time-memory tradeoff method

 Funding Agency Grant Number Russian Science Foundation 14-50-00005

DOI: https://doi.org/10.4213/dm1521

Full text: PDF file (484 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Discrete Mathematics and Applications, 2018, 28:5, 331–338

Bibliographic databases:

Document Type: Article
UDC: 519.212.2

Citation: A. M. Zubkov, A. A. Serov, “Estimates of the mean size of the subset image under composition of random mappings”, Diskr. Mat., 30:2 (2018), 27–36; Discrete Math. Appl., 28:5 (2018), 331–338

Citation in format AMSBIB
\Bibitem{ZubSer18} \by A.~M.~Zubkov, A.~A.~Serov \paper Estimates of the mean size of the subset image under composition of random mappings \jour Diskr. Mat. \yr 2018 \vol 30 \issue 2 \pages 27--36 \mathnet{http://mi.mathnet.ru/dm1521} \crossref{https://doi.org/10.4213/dm1521} \elib{http://elibrary.ru/item.asp?id=34940587} \transl \jour Discrete Math. Appl. \yr 2018 \vol 28 \issue 5 \pages 331--338 \crossref{https://doi.org/10.1515/dma-2018-0029} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000448699100006} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85056217416}