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Depending on the problem at hand, pre-order, post-order, and especially one of the number of subtrees − 1 in-order operations may be optional. Also, in practice more than one of pre-order, post-order, and in-order operations may be required. For example, when inserting into a ternary tree, a pre-order operation is performed by comparing items.
In computer science, an order statistic tree is a variant of the binary search tree (or more generally, a B-tree [1]) that supports two additional operations beyond insertion, lookup and deletion:
A problem related to the order-maintenance problem is the list-labeling problem in which instead of the order(X, Y) operation the solution must maintain an assignment of labels from a universe of integers {,, …,} to the elements of the set such that X precedes Y in the total order if and only if X is assigned a lesser label than Y.
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In these problems, constraints on the ordering are included one at a time, by modifying the PQ tree structure in such a way that it represents only orderings satisfying the constraint. Applications of PQ trees include creating a contig map from DNA fragments, [ 2 ] testing a matrix for the consecutive ones property, recognizing interval graphs ...
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