Nearly optimal static Las Vegas succinct dictionary

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations


Given a set S of n (distinct) keys from key space [U], each associated with a value from ς, the static dictionary problem asks to preprocess these (key, value) pairs into a data structure, supporting value-retrieval queries: for any given xg [U], valRet(x) must return the value associated with x if xg S, or return g¥ if xg‰ S. The special case where |ς|=1 is called the membership problem. The "textbook" solution is to use a hash table, which occupies linear space and answers each query in constant time. On the other hand, the minimum possible space to encode all (key, value) pairs is only OPT:= glg2(Un)+nlg2|ς|g‰ bits, which could be much less. In this paper, we design a randomized dictionary data structure using OPT+lgn+O(lglglglglgU) bits of space, and it has expected constant query time, assuming the query algorithm can access an external lookup table of size n0.001. The lookup table depends only on U, n and |ς|, and not the input. Previously, even for membership queries and U≤ nO(1), the best known data structure with constant query time requires OPT+n/lgn bits of space by Pagh (SIAM J. Comput. 2001) and PÇtraşcu (FOCS 2008); the best known using OPT+n0.999 space has query time O(lgn); the only known non-trivial data structure with OPT+n0.001 space has O(lgn) query time and requires a lookup table of size ≥ n2.99 (!). Our new data structure answers open questions by PÇtraşcu and Thorup.

Original languageEnglish (US)
Title of host publicationSTOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing
EditorsKonstantin Makarychev, Yury Makarychev, Madhur Tulsiani, Gautam Kamath, Julia Chuzhoy
PublisherAssociation for Computing Machinery
Number of pages13
ISBN (Electronic)9781450369794
StatePublished - Jun 8 2020
Event52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020 - Chicago, United States
Duration: Jun 22 2020Jun 26 2020

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017


Conference52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Software


  • Dictionary
  • Las vegas algorithm
  • Locally decodable source coding
  • Succinct data structure


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