Editing Binomial heap (section)

=== Decrease key ===
After '''decreasing''' the key of an element, it may become smaller than the key of its parent, violating the minimum-heap property. If this is the case, exchange the element with its parent, and possibly also with its grandparent, and so on, until the minimum-heap property is no longer violated. Each binomial tree has height at most <math>\log_2 n</math>, so this takes <math>O(\log n)</math> time.<ref name="clrs" /> However, this operation requires that the representation of the tree include pointers from each node to its parent in the tree, somewhat complicating the implementation of other operations.<ref name="brown" />