The Urinal Problem

  • Evangelos Kranakis
  • Danny Krizanc
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6099)


A man walks into a men’s room and observes n empty urinals. Which urinal should he pick so as to maximize his chances of maintaining privacy, i.e., minimize the chance that someone will occupy a urinal beside him? In this paper, we attempt to answer this question under a variety of models for standard men’s room behavior. Our results suggest that for the most part one should probably choose the urinal furthest from the door (with some interesting exceptions). We also suggest a number of variations on the problem that lead to many open problems.


Physical Privacy Urinal Problem Interesting Exception Toilet Paper Interesting Open Question 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    American Restroom Association, Public Restroom Design Issues,
  2. 2.
    Decker, D.: A Woman’s Guide on How to Pee Standing Up,
  3. 3.
    Flajolet, P.: A Seating Arrangement Problem,
  4. 4.
    Freedman, D., Shepp, L.: An Unfriendly Seating Arrangement Problem. SIAM Review 4, 150 (1962)CrossRefGoogle Scholar
  5. 5.
    Friedman, H.D., Rothman, D.: Solution to An Unfriendly Seating Arrangement Problem. SIAM Review 6, 180–182 (1964)CrossRefGoogle Scholar
  6. 6.
    Georgiou, K., Kranakis, E., Krizanc, D.: Random Maximal Independent Sets and the Unfriendly Theater Arrangement Problem. Discrete Mathematics 309, 5120–5129 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Hoffman, L.: Computers and Privacy: A Survey. Computing Surveys 1, 85–103 (1969)CrossRefGoogle Scholar
  8. 8.
    International Code Council, International Plumbing Code (2009)Google Scholar
  9. 9.
    Keane, M., Kranakis, E., Krizanc, D., Narayanan, L.: Routing on Delay Tolerant Sensor Networks. In: Algosensors 2009, pp. 155–166 (2009)Google Scholar
  10. 10.
    Kleinrock, L.: Queueing Systems, Volume 1: Theory. Wiley, Hoboken (1975)Google Scholar
  11. 11.
    Knuth, D.: The Toilet Paper Problem. American Math. Monthly 91, 365–370 (1984)CrossRefMathSciNetGoogle Scholar
  12. 12.
    MacKenzie, J.K.: Sequential Filling of a Line by Intervals Placed at Random and Its Application to Linear Absorption. Journal of Chemical Physics 37, 723–728 (1962)CrossRefGoogle Scholar
  13. 13.
    Paola, C.: A Survey of Obnoxious Facility Location Problems. TR-99-11, University of Pisa, Dept. of Informatics (1999)Google Scholar
  14. 14.
    Ross, S.M.: Stochastic Processes, 2nd edn. John Wiley & Sons, Inc., Chichester (1996)zbMATHGoogle Scholar
  15. 15.
    Soifer, S.: The Evolution of the Bathroom and the Implications for Paruresis,
  16. 16.
    Vogt, R., Nascimento, M.A., Harns, J.: On the Tradeoff between User-Location Privacy and Queried-Location Privacy in Wireless Sensor Networks. In: AdHoc Now 2009, pp. 241–254 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Evangelos Kranakis
    • 1
  • Danny Krizanc
    • 2
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.Department of Mathematics and Computer ScienceWesleyan UniversityMiddletownUSA

Personalised recommendations