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Haystack hunting hints and locker room communication

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Czumaj, Artur, Kontogeorgiou, George and Paterson, Michael S. (2021) Haystack hunting hints and locker room communication. In: 48th International Colloquium on Automata, Languages and Programming (ICALP 2021), Virtual, Scotland, 12-16 Jul 2021. Published in: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021), 198 58 : 1-58: 20. ISBN 9783959771955. ISSN 1868-8969. doi:10.4230/LIPIcs.ICALP.2021.58

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Official URL: https://doi.org/10.4230/LIPIcs.ICALP.2021.58

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Abstract

We want to efficiently find a specific object in a large unstructured set, which we model by a random n-permutation, and we have to do it by revealing just a single element. Clearly, without any help this task is hopeless and the best one can do is to select the element at random, and achieve the success probability 1/n. Can we do better with some small amount of advice about the permutation, even without knowing the object sought? We show that by providing advice of just one integer in {0, 1, . . . , n−1}, one can improve the success probability considerably, by a Θ(log n/log log n) factor.

We study this and related problems, and show asymptotically matching upper and lower bounds for their optimal probability of success. Our analysis relies on a close relationship of such problems to some intrinsic properties of random permutations related to the rencontres number.

Item Type: Conference Item (Paper)
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 (Please use QA76 Electronic Computers. Computer Science)
Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions: Faculty of Science, Engineering and Medicine > Science > Computer Science
Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Permutations, Computational complexity, Machine theory -- Mathematical models, Discrete mathematics
Series Name: Leibniz International Proceedings in Informatics (LIPIcs)
Journal or Publication Title: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Publisher: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik
ISBN: 9783959771955
ISSN: 1868-8969
Official Date: 2 July 2021
Dates:
DateEvent
2 July 2021Published
21 April 2021Accepted
Volume: 198
Page Range: 58 : 1-58: 20
DOI: 10.4230/LIPIcs.ICALP.2021.58
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
UNSPECIFIEDUniversity of Warwickhttp://dx.doi.org/10.13039/501100000741
UNSPECIFIEDIBM Center for the Business of Governmenthttp://dx.doi.org/10.13039/100014026
EP/V01305X/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
Doctoral Training Partnership[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
Conference Paper Type: Paper
Title of Event: 48th International Colloquium on Automata, Languages and Programming (ICALP 2021)
Type of Event: Conference
Location of Event: Virtual, Scotland
Date(s) of Event: 12-16 Jul 2021
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