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Predecessor on the Ultra-Wide Word RAM

Authors Philip Bille , Inge Li Gørtz , Tord Stordalen

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Philip Bille
  • DTU Compute, Technical University of Denmark, Lyngby, Denmark
Inge Li Gørtz
  • DTU Compute, Technical University of Denmark, Lyngby, Denmark
Tord Stordalen
  • DTU Compute, Technical University of Denmark, Lyngby, Denmark


We thank the anonymous reviewers for their comments, which improved the presentation of the article.

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Philip Bille, Inge Li Gørtz, and Tord Stordalen. Predecessor on the Ultra-Wide Word RAM. In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 18:1-18:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


We consider the predecessor problem on the ultra-wide word RAM model of computation, which extends the word RAM model with ultrawords consisting of w² bits [TAMC, 2015]. The model supports arithmetic and boolean operations on ultrawords, in addition to scattered memory operations that access or modify w (potentially non-contiguous) memory addresses simultaneously. The ultra-wide word RAM model captures (and idealizes) modern vector processor architectures. Our main result is a simple, linear space data structure that supports predecessor in constant time and updates in amortized, expected constant time. This improves the space of the previous constant time solution that uses space in the order of the size of the universe. Our result is based on a new implementation of the classic x-fast trie data structure of Willard [Inform. Process. Lett. 17(2), 1983] combined with a new dictionary data structure that supports fast parallel lookups.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
  • Ultra-wide word RAM model
  • predecessor
  • word-level parallelism


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