Some of the above structures also support a \(\mathtt{decreaseKey(u,y)}\) operation in which the value stored at node \(\mathtt{u}\) is decreased to \(\mathtt{y}\). (It is a pre-condition that \(\math...Some of the above structures also support a \(\mathtt{decreaseKey(u,y)}\) operation in which the value stored at node \(\mathtt{u}\) is decreased to \(\mathtt{y}\). (It is a pre-condition that \(\mathtt{y}\le\texttt{u.x}\).) In most of the preceding structures, this operation can be supported in \(O(\log \mathtt{n})\) time by removing node \(\mathtt{u}\) and adding \(\mathtt{y}\).
