# Hollow Heaps

arXiv: https://arxiv.org/abs/1510.06535 · HTML: https://mlsanity.com/paper/1510.06535/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2015.

## Built on by (most cited first, 1 of 1)

- [A Structural Complexity Analysis of Hierarchical Task Network Planning](https://mlsanity.com/paper/2401.14174/) (2024)

## Abstract (arXiv)

We introduce the hollow heap, a very simple data structure with the same amortized efficiency as the classical Fibonacci heap. All heap operations except delete and delete-min take O(1) time, worst case as well as amortized; delete and delete-min take O(log n) amortized time on a heap of n items. Hollow heaps are by far the simplest structure to achieve this. Hollow heaps combine two novel ideas: the use of lazy deletion and re-insertion to do decrease-key operations, and the use of a dag (directed acyclic graph) instead of a tree or set of trees to represent a heap. Lazy deletion produces hollow nodes (nodes without items), giving the data structure its name.