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<H1>little-o notation</H1>
<P>
(definition)

<P>
<strong>Definition:</strong>
A theoretical measure of the execution of an <a href="algorithm.html" tppabs="http://hissa.nist.gov/dads/HTML/algorithm.html"><em>algorithm</em></a>, usually the time or memory needed, given the problem size n, which is usually the number of items.  Informally, saying some equation f(n) = o(g(n)) means f(n) becomes insignificant relative to g(n) as n approaches infinity.  More formally it means for all c &gt; 0, there exists some k &gt; 0 such that 0  <img src="leq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/leq.gif" border=0 height=7  width=14 alt="less than or equal to"> f(n) &lt; cg(n) for all n  <img src="geq.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/geq.gif" border=0 height=7  width=14 alt="greater than or equal to"> k. The value of k must not depend on n, but may depend on c.
<P><strong>See also</strong>
<a href="bigOnotation.html" tppabs="http://hissa.nist.gov/dads/HTML/bigOnotation.html"><em>big-O notation</em></a>.
<P><em>Note:
As an example, 3n + 4 is o(n<sup>2</sup>)  since for any c we can choose  k &gt; (3+ <img src="sqrt.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/sqrt.gif"   border=0 height=15 width=12 alt="square root of">(9+16c))/2c.  3n + 4 is not o(n). o(f(n)) is an upper bound which is not <a href="asymptghtbnd.html" tppabs="http://hissa.nist.gov/dads/HTML/asymptghtbnd.html"><em>asymptotically tight</em></a>.   <P> Strictly, the character is the lower case Greek letter omicron.</em>
<P>Author: <a href="terms.html#authorPEB" tppabs="http://hissa.nist.gov/dads/terms.html#authorPEB">PEB</a>

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Entry modified Fri Jan  7 09:56:59 2000.<BR>
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