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
Synchronization is the coordination of events to operate a system in unison. For example, the conductor of an orchestra keeps the orchestra synchronized or ''in time''. Systems that operate with all parts in synchrony are said to be synchronou ...
,
operating system
An operating system (OS) is system software that manages computer hardware, software resources, and provides common services for computer programs.
Time-sharing operating systems schedule tasks for efficient use of the system and may also in ...
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 deci ...
, and even
search and rescue
Search and rescue (SAR) is the search for and provision of aid to people who are in distress or imminent danger. The general field of search and rescue includes many specialty sub-fields, typically determined by the type of terrain the search ...
operations planning.
Deterministic rendezvous problem
The deterministic rendezvous problem is a variant of the rendezvous problem where the players, or ''robots'', must find each other by following a
deterministic
Determinism is a philosophical view, where all events are determined completely by previously existing causes. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and consi ...
sequence of instructions. Although each robot follows the same instruction sequence, a unique label assigned to each robot is used for
symmetry breaking
In physics, symmetry breaking is a phenomenon in which (infinitesimally) small fluctuations acting on a system crossing a critical point decide the system's fate, by determining which branch of a bifurcation is taken. To an outside observe ...
.
See also
*
Coordination game A coordination game is a type of simultaneous game found in game theory. It describes the situation where a player will earn a higher payoff when they select the same course of action as another player. The game is not one of pure conflict, which r ...
*
Dining philosophers problem
In computer science, the dining philosophers problem is an example problem often used in concurrent algorithm design to illustrate synchronization issues and techniques for resolving them.
It was originally formulated in 1965 by Edsger Dijkstra ...
*
Probabilistic algorithm
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performan ...
*
Search games
A search game is a two-person zero-sum game which takes place in a set called the search space. The searcher can choose any continuous trajectory subject to a maximal velocity constraint. It is always assumed that neither the searcher nor the hider ...
*
Sleeping barber problem In computer science, the sleeping barber problem is a classic inter-process communication and synchronization problem that illustrates the complexities that arise when there are multiple operating system processes.
The problem was originally pro ...
*
Superrationality
In economics and game theory, a participant is considered to have superrationality (or renormalized rationality) if they have perfect rationality (and thus maximize their utility) but assume that all other players are superrational too and that a s ...
*
Symmetry breaking
In physics, symmetry breaking is a phenomenon in which (infinitesimally) small fluctuations acting on a system crossing a critical point decide the system's fate, by determining which branch of a bifurcation is taken. To an outside observe ...
References
{{game theory
Cooperative games