preorder

English Wikipedia has an article on:

preorder

Wikipedia

From pre- +‎ order.

preorder (third-person singular simple present preorders, present participle preordering, simple past and past participle preordered)

1. (transitive) To order (goods or services) in advance, before they are available.
2. (transitive) To sort or arrange beforehand.

preorder (plural preorders)

1. An order for goods or services placed in advance.
2. (set theory, order theory) A binary relation that is reflexive and transitive.

   The relation of logical implication over sentences is an example of a preorder.

   • 2002, Yves Nievergelt, Foundations of Logic and Mathematics‎, Springer (Birkhäuser), page 152:

     Example 436 For each set ${\displaystyle A}$, the relation ${\displaystyle \subseteq }$ is a preorder on ${\displaystyle {\mathcal {P}}(A)}$.

   • 2010, S. Kaci, “Refined Preference-Based Argumentation Frameworks”, in Pietro Baroni, F. Cerutti, M. Giacomin, G. R. Simari, editors, Computational Models of Argument: Proceedings of COMMA 2010, IOS Press, page 306:

     Let us first compare ${\displaystyle S_{1}}$, ${\displaystyle S_{2}}$ and ${\displaystyle S_{3}}$ w.r.t. the partial preorder ${\displaystyle \succeq }$.

   • 2000, Jean-Charles Pomerol, Sergio Barba-Romero, Multicriterion Decision in Management: Principles and Practice, Springer, Softcover, page 58,

     It can easily be verified that the above relation is a preorder, i.e. that it is reflexive and transitive.

• (binary relation that is reflexive and transitive): quasiorder

• (binary relation that is reflexive and transitive):
  • partial order
    • total order
      • well-order
  • equivalence relation

• preorder algebra
• preorder atom
• preorder functor
• strict preorder

• preordered set

preorder (not comparable)

1. (computing theory, of a traversal of a tree) Such that, recursively, the root is visited before the left and right subtrees.
   • 2002, Gabriel Valiente, Algorithms on Trees and Graphs, Springer, page 115:

     Now, the preorder traversal of a tree can be constructed from the preorder traversals of the subtrees rooted at the children of the root of the tree.

   • 2006, ISRD Group, Data Structures Using C, Tata McGraw-Hill Education, page 254:

     In the program given above, tree is constructed and is traversed in inorder, preorder and postorder traversal.

   • 2011, Ananda Rao Akepogu, Radhika Raju Palagiri, Data Structures and Algorithms Using C++, Pearson Education India, page 9.16,

     The preorder traversal visits a node first after which it traverses its left subtree and then traverses its right subtree.

• depth-first

• inorder
• postorder