Haystack Hunting Hints and Locker Room Communication

Authors Artur Czumaj, George Kontogeorgiou, Mike Paterson

Thumbnail PDF


  • Filesize: 1.61 MB
  • 20 pages

Document Identifiers

Author Details

Artur Czumaj
  • Department of Computer Science and DIMAP, University of Warwick, Coventry, UK
George Kontogeorgiou
  • Mathematics Institute, University of Warwick, Coventry, UK
Mike Paterson
  • Department of Computer Science and DIMAP, University of Warwick, Coventry, UK

Cite AsGet BibTex

Artur Czumaj, George Kontogeorgiou, and Mike Paterson. Haystack Hunting Hints and Locker Room Communication. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 58:1-58:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Permutations and combinations
  • Theory of computation → Communication complexity
  • Random permutations
  • Search
  • Communication complexity


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Micah Adler, Soumen Chakrabarti, Michael Mitzenmacher, and Lars Eilstrup Rasmussen. Parallel randomized load balancing. In Proceedings of the 27th Annual ACM Symposium on Theory of Computing (STOC), pages 238-247, 1995. Google Scholar
  2. Béla Bollobás. Random Graphs. Cambridge University Press, Cambridge, UK, 2nd edition, 2001. Google Scholar
  3. Carlo Emilio Bonferroni. Teoria statistica delle classi e calcolo delle probabilità. Pubblicazioni del R Istituto Superiore di Scienze Economiche e Commerciali di Firenze, 8:3-62, 1936. Google Scholar
  4. Joe P. Buhler. Hat tricks. The Mathematical Intelligencer, 24(4):44-49, 2002. Google Scholar
  5. Eucene Curtin and Max Warshauer. The locker puzzle. The Mathematical Intelligencer, 28(1):28-31, March 2006. Google Scholar
  6. Devdatt P. Dubhashi and Desh Ranjan. Balls and bins: A study in negative dependence. Random Structures and Algorithms, 13(2):99-124, 1998. Google Scholar
  7. Anna Gál and Peter Bro Miltersen. The cell probe complexity of succinct data structures. In Proceedings of the 30th Annual International Colloquium on Automata, Languages and Programming (ICALP), pages 332-344, 2003. Google Scholar
  8. Navin Goyal and Michael E. Saks. A parallel search game. Random Structures and Algorithms, 27(2):227-234, 2005. Google Scholar
  9. Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley, Reading, MA, 2nd edition, 1994. Google Scholar
  10. Donald E. Knuth. The Art of Computer Programming: Sorting and Searching, volume III. Addison-Wesley, Reading, MA, 2nd edition, 1998. Google Scholar
  11. Michael Mitzenmacher and Eli Upfal. Probability and Computing: Randomized and Probabilistic Techniques in Algorithms and Data Analysis. Cambridge University Press, Cambridge, UK, 2nd edition, 2017. Google Scholar
  12. Martin Raab and Angelika Steger. "Balls into bins" - A simple and tight analysis. In Proceedings of the 2nd International Workshop on Randomization and Approximation Techniques in Computer Science (RANDOM), pages 159-170, 1998. Google Scholar
  13. John Riordan. An Introduction to Combinatorial Analysis. John Wiley & Sons, Inc., New York, NY, 1958. Google Scholar
  14. Peter Winkler. Names in boxes puzzle. College Mathematics Journal, 37(4):260, 285, 289, September 2006. Google Scholar
  15. Peter Winkler. Mathematical Mind-Benders. A K Peters, Ltd., Wellesley, MA, 2007. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail