Big Omicron and big Omega and big Theta

  title={Big Omicron and big Omega and big Theta},
  author={Donald Ervin Knuth},
  journal={SIGACT News},
  • D. Knuth
  • Published 1 April 1976
  • Education
  • SIGACT News
Most of us have gotten accustomed to the idea of using the notation O(f(n)) to stand for any function whose magnitude is upper-bounded by a constant times f(n) , for all large n. Sometimes we also need a corresponding notation for lower-bounded functions, i.e., those functions which are at least as large as a constant times f(n) for all large n. Unfortunately~ people have occasionally been using the O-notation for lower bounds, for example when they reject a particular sorting method "because… 

What does O(n) mean

The traditional notation is defended here, despite the fact that the new notation calls for extending arithmetic operations from functions to sets of functions, and gives rise, as Gilles Brassard honestly and immediately acknowledges, to a new type of ambiguous expressions.

The Big-O of Mathematics and Computer Science

  • F. MalaRouf Ali
  • Computer Science
    Journal of Applied Mathematics and Computation
  • 2022
It is shown, using examples, how the Big-O notation could turn out to be a better, easier and more informative notation compared to the limit notation of a function.

Topics of Mathematics in Cryptology Asymptotic Notation

And now you ask: What is the running time of the main program in terms of n? Given the above, this is difficult to answer. f(a) makes a2 multiplications. How much time does a multiplication take?

Two decades of applied Kolmogorov complexity: in memoriam Andrei Nikolaevich Kolmogorov 1903-87

  • Ming LiP. Vitányi
  • Computer Science
    [1988] Proceedings. Structure in Complexity Theory Third Annual Conference
  • 1988
The authors provide an introduction to the main ideas of Kolmogorov complexity and survey the wealth of useful applications of this notion. It is based on a theory of information content of strings,

Crusade for a better notation

In a well-known SIGACT/NEWS paper, Knuth sets forth the asymptotic notation by which the authors all now live and proposes that members of SIGACT adopt the O, Ω and Θ notations unless a better alternative can be found reasonably soon.

TME Volume 13, Number 3

The decimal expansions of the numbers 1{n (such as 1{3 “ 0.3333..., 1{7 “ 0.142857...) are most often viewed as tools for approximating quantities to a desired degree of accuracy. The aim of this

Series misdemeanors

Issues such as avoiding unnecessary restrictions such as prohibiting negative or fractional requested orders, the pros and cons of displaying results with explicit infectious error terms, efficient data structures, and algorithms that efficiently give users exactly the order or number of nonzero terms they request are discussed.

Foreword This chapter is based on lecture notes from coding theory courses taught by Venkatesan

1. Asymptotics of codes: Given > 0 express the rate of the best family of binary codes of relative distance 1 2 − , you can (a) construct, and (b) show the existence of. Express the rate in big-Oh

Remarks on Abstracto

High-level programming languages have had a direct influence on the presentation of algorithms in the literature and many an author now employs a kind of pidgin ALGOL to express himself.

How Many Steps Still Left to \bfitx *? \ast

. The high speed of x k \rightarrow x \ast \in \BbbR is usually measured using the C -, Q -, or R -orders: By connecting them to the natural, term-by-term comparison of the errors of two



Some problems of diophantine approximation

Let 0 be an irrational number, and a any number between 0 and 1 (0 included). Then it is well known that it is possible to find a sequence of positive integers w<i, n2, n3, ... such that (nr0) —>a as

An Algorithm for the Computation of Linear Forms

An algorithm is presented here which implies that every polynomial of degree n with at most s distinct coefficients can be realized with O(n/\log _s n) operations.

Die Analytische Zahlentheorie. Zahlentheorie, pt

  • Die Analytische Zahlentheorie. Zahlentheorie, pt

Leipzig: B. G. Teubner

  • Leipzig: B. G. Teubner
  • 1894

Savage presents therein a generalization of the Four Russians' Algorithm, several applications of it, and a counting argument lower bound similar to Moon and Moser's. Sincerely

  • Savage presents therein a generalization of the Four Russians' Algorithm, several applications of it, and a counting argument lower bound similar to Moon and Moser's. Sincerely