About
A Partially ordered structure is a data structure where not every pair of elements needs to be comparable (compared).
Articles Related
Example
Genealogy
A collection of people ordered by genealogical descendancy:
- Some pairs of people bear the descendant-ancestor relationship,
- But other pairs of people are incomparable, with neither being a descendant of the other.
Heap
A Heap is also a sort of partially ordered structure. (ie the parent node should have a bigger value than the child)
(By Ermishin - Own work, CC BY-SA 3.0)
Properties
A partial order is any binary relation that is:
- reflexive (each element is comparable to itself),
- antisymmetric (no two different elements precede each other),
- transitive (the start of a chain of precedence relations must precede the end of the chain).