Oblivious parallel tight compaction

Gilad Asharov, Ilan Komargodski, Wei Kai Lin, Enoch Peserico, Elaine Shi

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

7 Scopus citations

Abstract

In tight compaction one is given an array of balls some of which are marked 0 and the rest are marked 1. The output of the procedure is an array that contains all of the original balls except that now the 0-balls appear before the 1-balls. In other words, tight compaction is equivalent to sorting the array according to 1-bit keys (not necessarily maintaining order within same-key balls). Tight compaction is not only an important algorithmic task by itself, but its oblivious version has also played a key role in recent constructions of oblivious RAM compilers. We present an oblivious deterministic algorithm for tight compaction such that for input arrays of n balls requires O(n) total work and O(log n) depth. Our algorithm is in the Exclusive-Read-Exclusive-Write Parallel-RAM model (i.e., EREW PRAM, the most restrictive PRAM model), and importantly we achieve asymptotical optimality in both total work and depth. To the best of our knowledge no earlier work, even when allowing randomization, can achieve optimality in both total work and depth.

Original languageEnglish
Title of host publication1st Conference on Information-Theoretic Cryptography, ITC 2020
EditorsYael Tauman Kalai, Adam D. Smith, Daniel Wichs
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771511
DOIs
StatePublished - 1 Jun 2020
Event1st Conference on Information-Theoretic Cryptography, ITC 2020 - Virtual, Boston, United States
Duration: 17 Jun 202019 Jun 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume163
ISSN (Print)1868-8969

Conference

Conference1st Conference on Information-Theoretic Cryptography, ITC 2020
Country/TerritoryUnited States
CityVirtual, Boston
Period17/06/2019/06/20

Bibliographical note

Publisher Copyright:
© Gilad Asharov, Ilan Komargodski, Wei-Kai Lin, Enoch Peserico, and Elaine Shi; licensed under Creative Commons License CC-BY

Funding

Funding Wei-Kai Lin: Wei-Kai Lin supported by NSF CNS-1453634, an ONR YIP award, a Packard Fellowship, and a DARPA Brandeis grant. Elaine Shi: Elaine Shi supported by NSF CNS-1453634, an ONR YIP award, a Packard Fellowship, and a DARPA Brandeis grant.

FundersFunder number
National Science FoundationCNS-1453634
Office of Naval Research
Defense Advanced Research Projects Agency

    Keywords

    • EREW PRAM
    • Oblivious tight compaction
    • Parallel oblivious RAM

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