(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*.

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Entry modified 17 December 2004.

HTML page formatted Fri Feb 23 10:06:08 2018.

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: https://www.nist.gov/dads/HTML/partialorder.html