(definition)

**Definition:**
(1) Any function which is the sum of constants times powers of a logarithm of the argument: f(x)=Σ_{i=0}^{k}c_{i}log^{pi} x. (2) In complexity theory, the measure of computation, m(n) (usually execution time or memory space), is bounded by a polylogarithmic function of the problem size, n. More formally m(n) = *O(log ^{k} n)*.

**See also**
*logarithmic*, *polynomial*, *exponential*.

Author: PEB

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Entry modified 17 December 2004.

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Cite this as:

Paul E. Black, "polylogarithmic", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/polylogarith.html