The rendezvous dilemma is a logical dilemma, typically formulated in this way:
:Two people have a date in a park they have never been to before. Arriving separately in the park, they are both surprised to discover that it is a huge area and consequently they cannot find one another. In this situation each person has to choose between waiting in a fixed place in the hope that the other will find them, or else starting to look for the other in the hope that ''they'' have chosen to wait somewhere.
If they both choose to wait, they will never meet. If they both choose to walk there are chances that they meet and chances that they do not. If one chooses to wait and the other chooses to walk, then there is a theoretical certainty that they will meet eventually; in practice, though, it may take too long for it to be guaranteed. The question posed, then, is: what strategies should they choose to maximize their probability of meeting?
Examples of this class of problems are known as rendezvous problems. These problems were first introduced informally by
Steve Alpern
Professor Steve Alpern is a professor of Operational Research at the University of Warwick, where he recently moved after working for many years at the London School of Economics. His early work was mainly in the area of dynamical systems and er ...
in 1976, and he formalised the continuous version of the problem in 1995. This has led to much recent research in rendezvous search. Even the symmetric rendezvous problem played in ''n'' discrete locations (sometimes called the ''Mozart Cafe Rendezvous Problem'') has turned out to be very difficult to solve, and in 1990
Richard Weber and Eddie Anderson conjectured the optimal strategy. In 2012 the conjecture was proved for ''n'' = 3 by
Richard Weber. This was the first non-trivial symmetric rendezvous search problem to be fully solved. Note that the corresponding asymmetric rendezvous problem has a simple optimal solution: one player stays put and the other player visits a random permutation of the locations.
As well as being problems of theoretical interest, rendezvous problems include real-world problems with applications in the fields of
synchronization,
operating system
An operating system (OS) is system software that manages computer hardware, software resources, and provides common daemon (computing), services for computer programs.
Time-sharing operating systems scheduler (computing), schedule tasks for ef ...
design,
operations research
Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve dec ...
, and even