(definition)

**Definition:**
An order defined for some, but not necessarily all, pairs of items. For instance, the *sets* {a, b} and {a, c, d} are *subsets* of {a, b, c, d}, but neither is a subset of the other. So "subset of" is a partial order on sets.

**Formal Definition:** A partial order is a *binary relation* that is *reflexive*, *transitive*, and *antisymmetric*.

**See also**
*total order*, *poset*.

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 17 December 2004.

HTML page formatted Tue May 6 13:48:56 2014.

Cite this as:

Paul E. Black and Paul J. Tanenbaum, "partial order", 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/partialorder.html