Partition-based Simple Heaps
🤖 AI Summary
This work addresses the design of priority queues supporting efficient insert, decrease-key, and extract-min operations. It proposes a novel partition-based heap structure composed of $O(\log n)$ doubly linked lists that are internally unordered yet globally sorted. By introducing a new strategy of binary partitioning and merging of these lists—relying solely on elementary operations such as binary search and list concatenation—the paper pioneers the application of partitioning techniques to simple heap design. The resulting data structure achieves $O(\log \log n)$ amortized time for both insert and decrease-key operations, and $O(\log n)$ time for extract-min, thereby outperforming traditional heap structures in theoretical efficiency.
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
priority queue
data structure
amortized time
linked lists
heap
Innovation
Methods, ideas, or system contributions that make the work stand out.
partition-based heaps
priority queue
amortized complexity
linked list partitioning
decrease-key
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