(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 E. Black.

Entry modified 17 December 2004.

HTML page formatted Fri Mar 25 16:20:34 2011.

Cite this as:

Paul E. Black and Paul J. Tanenbaum, "partial order", in
*Dictionary of Algorithms and Data
Structures* [online], Paul E. Black, ed.,
U.S. National Institute of
Standards and Technology. 17 December 2004. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/partialorder.html