Dynamic Dictionaries for Multisets and Counting Filters with Constant Time Operations

Ioana O. Bercea, Guy Even

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We resolve the open problem posed by Arbitman, Naor, and Segev [FOCS 2010] of designing a dynamic dictionary for multisets in the following setting: (1) The dictionary supports multiplicity queries and allows insertions and deletions to the multiset. (2) The dictionary is designed to support multisets of cardinality at most n (i.e., including multiplicities). (3) The space required for the dictionary is (1+o(1))·nlogun+Θ(n) bits, where u denotes the cardinality of the universe of the elements. This space is 1 + o(1 ) times the information-theoretic lower bound for static dictionaries over multisets of cardinality n if u= ω(n). (4) All operations are completed in constant time in the worst case with high probability in the word RAM model. A direct consequence of our construction is the first dynamic counting filter (i.e., a dynamic data structure that supports approximate multiplicity queries with a one-sided error) that, with high probability, supports operations in constant time and requires space that is 1 + o(1 ) times the information-theoretic lower bound for filters plus O(n) bits. The main technical component of our solution is based on efficiently storing variable-length bounded binary counters and its analysis via weighted balls-into-bins experiments in which the weight of a ball is logarithmic in its multiplicity.

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 17th International Symposium, WADS 2021, Proceedings
EditorsAnna Lubiw, Mohammad Salavatipour
PublisherSpringer Science and Business Media Deutschland GmbH
Pages144-157
Number of pages14
ISBN (Print)9783030835071
DOIs
StatePublished - 2021
Event17th International Symposium on Algorithms and Data Structures, WADS 2021 - Virtual, Online
Duration: 9 Aug 202111 Aug 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12808 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference17th International Symposium on Algorithms and Data Structures, WADS 2021
CityVirtual, Online
Period9/08/2111/08/21

Keywords

  • Ditionaries
  • Filters
  • Multisets

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