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Hollow Heaps

22 Oct 2015arXiv:1510.06535links table onlyarchive 2025-07-28

Thomas Dueholm Hansen, Haim Kaplan, Robert E. Tarjan, Uri Zwick

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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(logn) 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.

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