@article{79eba4a0c92c4379a9756d22a5d5d2a7,

title = "Dynamic Dictionaries for Multisets and Counting Filters with Constant Time Operations",

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.",

keywords = "Approximate membership, Data structures, Dictionaries, Membership, Multisets",

author = "Bercea, {Ioana O.} and Guy Even",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2023",

month = jun,

doi = "10.1007/s00453-022-01057-0",

language = "אנגלית",

volume = "85",

pages = "1786--1804",

journal = "Algorithmica",

issn = "0178-4617",

publisher = "Springer New York",

number = "6",

}