Ordinal Data - Partially Order

About

A Partially ordered structure is a data structure where not every pair of elements needs to be comparable (compared).

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)

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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).

Documentation / Reference


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