@inproceedings{583785dfaf0c443683b1452751d3cf7d,

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 = "Ditionaries, Filters, Multisets",

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

note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.; null ; Conference date: 09-08-2021 Through 11-08-2021",

year = "2021",

doi = "10.1007/978-3-030-83508-8_11",

language = "אנגלית",

isbn = "9783030835071",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Science and Business Media Deutschland GmbH",

pages = "144--157",

editor = "Anna Lubiw and Mohammad Salavatipour",

booktitle = "Algorithms and Data Structures - 17th International Symposium, WADS 2021, Proceedings",

address = "גרמניה",

}