License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.58
URN: urn:nbn:de:0030-drops-141270
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Czumaj, Artur ; Kontogeorgiou, George ; Paterson, Mike

Haystack Hunting Hints and Locker Room Communication

LIPIcs-ICALP-2021-58.pdf (2 MB)


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.

BibTeX - Entry

  author =	{Czumaj, Artur and Kontogeorgiou, George and Paterson, Mike},
  title =	{{Haystack Hunting Hints and Locker Room Communication}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{58:1--58:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-141270},
  doi =		{10.4230/LIPIcs.ICALP.2021.58},
  annote =	{Keywords: Random permutations, Search, Communication complexity}

Keywords: Random permutations, Search, Communication complexity
Collection: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue Date: 2021
Date of publication: 02.07.2021

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