High-Probability List-Recovery, and Applications to Heavy Hitters

Dean Doron, Mary Wootters

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

Abstract

An error correcting code C: Σk → Σn is efficiently list-recoverable from input list size ℓ if for any sets L1,..., Ln ⊆ Σ of size at most ℓ, one can efficiently recover the list L = {x ∈ Σk : ∀j ∈ [n], C(x)j ∈ Lj}. While list-recovery has been well-studied in error correcting codes, all known constructions with “efficient” algorithms are not efficient in the parameter ℓ. In this work, motivated by applications in algorithm design and pseudorandomness, we study list-recovery with the goal of obtaining a good dependence on ℓ. We make a step towards this goal by obtaining it in the weaker case where we allow a randomized encoding map and a small failure probability, and where the input lists are derived from unions of codewords. As an application of our construction, we give a data structure for the heavy hitters problem in the strict turnstile model that, for some parameter regimes, obtains stronger guarantees than known constructions.

Original languageEnglish
Title of host publication49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022
EditorsMikolaj Bojanczyk, Emanuela Merelli, David P. Woodruff
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772358
DOIs
StatePublished - 1 Jul 2022
Event49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022 - Paris, France
Duration: 4 Jul 20228 Jul 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume229
ISSN (Print)1868-8969

Conference

Conference49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022
Country/TerritoryFrance
CityParis
Period4/07/228/07/22

Keywords

  • Heavy Hitters
  • List recoverable codes
  • high-dimensional expanders

ASJC Scopus subject areas

  • Software

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