Hollow Heaps

  • Thomas Dueholm Hansen
  • Haim KaplanEmail author
  • Robert E. Tarjan
  • Uri Zwick
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9134)


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. 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.


Amortize Time Fibonacci Heap Virtual Parent Full Node Full Root 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Thomas Dueholm Hansen
    • 1
  • Haim Kaplan
    • 2
    Email author
  • Robert E. Tarjan
    • 3
    • 4
  • Uri Zwick
    • 2
  1. 1.Department of Computer ScienceAarhus UniversityAarhusDenmark
  2. 2.Blavatnik School of Computer ScienceTel Aviv UniversityTel Aviv-YafoIsrael
  3. 3.Department of Computer SciencePrinceton UniversityPrincetonUSA
  4. 4.Intertrust TechnologiesSunnyvaleUSA

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