Skip to main content Accessibility help

The rendezvous problem on discrete locations

  • E. J. Anderson (a1) and R. R. Weber (a1)


Two friends have become separated in a building or shopping mall and and wish to meet as quickly as possible. There are n possible locations where they might meet. However, the locations are identical and there has been no prior agreement where to meet or how to search. Hence they must use identical strategies and must treat all locations in a symmetrical fashion. Suppose their search proceeds in discrete time. Since they wish to avoid the possibility of never meeting, they will wish to use some randomizing strategy. If each person searches one of the n locations at random at each step, then rendezvous will require n steps on average. It is possible to do better than this: although the optimal strategy is difficult to characterize for general n, there is a strategy with an expected time until rendezvous of less than 0.829 n for large enough n. For n = 2 and 3 the optimal strategy can be established and on average 2 and 8/3 steps are required respectively. There are many tantalizing variations on this problem, which we discuss with some conjectures.


Corresponding author

Postal address for both authors: University of Cambridge, Department of Engineering, Management Studies Group, Mill Lane, Cambridge CB2 1RX, UK.


Hide All
Abramson, N. (1973) Packet switching with satellites. Proc. NCC, 695702.
Alpern, S. and Asic, M. (1986) Ambush strategies in search games on graphs. SIAM J. Control Optim. 24, 6675.
Anantharam, V. and Varaiya, P. (1986) An optimal strategy for a conflict resolution problem. Syst. Control Lett. 6, 329332.
Foreman, J. G. (1977) Differential search games with mobile hider. SIAM J. Control Optim. 15, 841856.
Gal, S. (1980) Search Games. Academic Press, San Francisco.
Mosteller, F. (1963) Fifty Challenging Problems in Probability with Solutions. Addison-Wesley, New York.
Ross, S. M. (1988) A simple proof of instability of a random-access communication channel. Prob. Eng. Inf. Sci. 2, 383385.
Schelling, T. C. (1960) The Strategy of Conflict. Oxford University Press.
Tobagi, F. A. (1980) Multi-access protocols in packet-communications systems. IEEE Trans. Commun. 28, 468488.
Weber, R. R. (1986) Optimal search for a randomly moving object. J. Appl. Prob. 23, 708717.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed