2026-07-21T23:50:42Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:16178 2024-03-06T10:57:05Z ddc:004 open_access

Predecessor on the Ultra-Wide Word RAM Bille, Philip Gørtz, Inge Li Stordalen, Tord Ultra-wide word RAM model predecessor word-level parallelism 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Philip Bille and Inge Li Gørtz and Tord Stordalen 2022 Is Part Of LIPIcs, Volume 227, 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SWAT.2022.18 urn:nbn:de:0030-drops-161786 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.18 eng https://creativecommons.org/licenses/by/4.0/legalcode