Therendezvous dilemma is a logical dilemma, typically formulated in this way:
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 asrendezvous problems. These problems were first introduced informally bySteve Alpern in 1976,[1] and he formalised the continuous version of the problem in 1995.[2] This has led to much recent research in rendezvous search.[3] Even the symmetric rendezvous problem played inn discrete locations (sometimes called theMozart Cafe Rendezvous Problem)[4] has turned out to be very difficult to solve, and in 1990Richard Weber and Eddie Anderson conjectured the optimal strategy.[5] In 2012 the conjecture was proved forn = 3 byRichard Weber.[6] This was the first non-trivial symmetric rendezvous search problem to be fully solved. 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 ofsynchronization,operating system design,operations research, and evensearch and rescue operations planning.
Thedeterministic rendezvous problem is a variant of the rendezvous problem where the players, orrobots, must find each other by following adeterministic sequence of instructions. Although each robot follows the same instruction sequence, a unique label assigned to each robot is used forsymmetry breaking.[7]
