Partition-based Simple Heaps

We introduce a new family of priority-queue data structures: partition-based simple heaps. The structures consist of $O(\log n)$ doubly-linked lists; order is enforced among data in different lists, but the individual lists are unordered. Our structures have amortized $O(\log n)$ time extract-min and amortized $O(\log \log n)$ time insert and decrease-key. The structures require nothing beyond binary search over $O(\log n)$ elements, as well as binary partitions and concatenations of linked lists in natural ways as the linked lists get too big or small. We present three different ways that these lists can be maintained in order to obtain the stated amortized running times.