Approximation of the size of the union

Shuji Jinbo, Akira Maruoka

Research output: Contribution to journalArticle

Abstract

Let k and n be integers with 1 ≤ h ≤ n; F(k, n) is the worst-case relative error generated in approximating the size of a finite system of n sets when the sizes of the intersections of all subsystems of at most k subsets are given. Linial et al. proposed a strategy to estimate F(k, n) and suggested that the strategy is applicable for the problem of counting the number of truth assignments for a DNF formula and the problem of calculating the permanent of a 0/1 matrix, both of which belong to the class of #P-complete problems. Although the time complexity increases as k increases, F(k, n) decreases their strategy. This paper gives elementary formulas that describe upper and lower bounds on F(k, n) for any k and n. The upper bound is better than the previous one when 2 ≤ n - k ≤ n/(8/loge n). Furthermore, F(k, n) = 1 + Θ(√nn-k-1/2n) is defined for any k and n such that n - k is at most a constant.

Original languageEnglish
Pages (from-to)11-23
Number of pages13
JournalSystems and Computers in Japan
Volume27
Issue number6
Publication statusPublished - Jun 1996

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Keywords

  • #P-complete
  • Approximation algorithms
  • Binomial coefficients
  • Polynomial approximation

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Hardware and Architecture
  • Information Systems
  • Theoretical Computer Science

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