Partition-based Simple Heaps

TL;DR

This paper introduces partition-based simple heaps, a new priority queue structure with efficient amortized operations, using multiple unordered linked lists organized by partitioning, offering improvements over traditional heaps.

Contribution

The paper presents a novel family of priority queues called partition-based simple heaps, with multiple unordered lists and efficient amortized operation times, achieved through simple list partitioning techniques.

Findings

Amortized O(log n) extract-min time

Amortized O(log log n) insert and decrease-key times

Structures require only binary search and list partitioning operations

Abstract

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.