implemented with pairing heaps \cite{fredman:pairingheap}. The pairing heaps
are known to perform surprisingly well in practice, but they still elude attempts
at complete theoretical analysis. So far the best results are those of Pettie
\cite{pettie:pairing}, who has proven that deletion of the minimum takes $\O(\log n)$
implemented with pairing heaps \cite{fredman:pairingheap}. The pairing heaps
are known to perform surprisingly well in practice, but they still elude attempts
at complete theoretical analysis. So far the best results are those of Pettie
\cite{pettie:pairing}, who has proven that deletion of the minimum takes $\O(\log n)$