Iceberg Hashing: Optimizing Many Hash-Table Criteria at Once

Michael A. Bender, Alex Conway, Martín Farach-Colton, William Kuszmaul, Guido Tagliavini

    Research output: Contribution to journalArticlepeer-review


    Despite being one of the oldest data structures in computer science, hash tables continue to be the focus of a great deal of both theoretical and empirical research. A central reason for this is that many of the fundamental properties that one desires from a hash table are difficult to achieve simultaneously; thus many variants offering different trade-offs have been proposed. This article introduces Iceberg hashing, a hash table that simultaneously offers the strongest known guarantees on a large number of core properties. Iceberg hashing supports constant-time operations while improving on the state of the art for space efficiency, cache efficiency, and low failure probability. Iceberg hashing is also the first hash table to support a load factor of up to 1−o(1) while being stable, meaning that the position where an element is stored only ever changes when resizes occur. In fact, in the setting where keys are Θ(log n) bits, the space guarantees that Iceberg hashing offers, namely that it uses at most log (Formula presented) + O(n log log n) bits to store n items from a universe U, matches a lower bound by Demaine et al. that applies to any stable hash table. Iceberg hashing introduces new general-purpose techniques for some of the most basic aspects of hash-table design. Notably, our indirection-free technique for dynamic resizing, which we call waterfall addressing, and our techniques for achieving stability and very-high probability guarantees, can be applied to any hash table that makes use of the front-yard/backyard paradigm for hash table design.

    Original languageEnglish (US)
    Article number40
    JournalJournal of the ACM
    Issue number6
    StatePublished - Nov 30 2023


    • dynamic resizing
    • Hashing
    • stability

    ASJC Scopus subject areas

    • Software
    • Control and Systems Engineering
    • Information Systems
    • Hardware and Architecture
    • Artificial Intelligence


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