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<H1>logarithmic</H1>
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(definition)
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<strong>Definition:</strong>
(1) Any function which is the sum of constants times a logarithm of the argument: f(x)= <img src="Sigma.gif" tppabs="http://hissa.nist.gov/dads/HTML/Images/Sigma.gif" border=0 height=10 width=8 alt="Capital Sigma"><sub>i=0</sub><sup>k</sup>c<sub>i</sub> log x. (2) In complexity theory, the measure of computation, m(n) (usually execution time or memory space), is bounded by a logarithmic function of the problem size, n. More formally m(n) = <a href="bigOnotation.html" tppabs="http://hissa.nist.gov/dads/HTML/bigOnotation.html"><em>O( log n)</em></a>. (3) Sometimes imprecisely used to mean <a href="polylogarith.html" tppabs="http://hissa.nist.gov/dads/HTML/polylogarith.html"><em>polylogarithmic</em></a>.
<P><strong>See also</strong>
<a href="linear.html" tppabs="http://hissa.nist.gov/dads/HTML/linear.html"><em>linear</em></a>, <a href="polynomial.html" tppabs="http://hissa.nist.gov/dads/HTML/polynomial.html"><em>polynomial</em></a>, <a href="exponential.html" tppabs="http://hissa.nist.gov/dads/HTML/exponential.html"><em>exponential</em></a>.
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Entry modified Wed Sep 22 16:53:55 1999.<BR>
HTML page formatted Wed Dec 22 09:35:46 1999.
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