Oblivious collaboration

We introduce oblivious protocols, a new framework for distributed computation with limited communication. Within this model we consider the musical chairs task MC(n,m), involving n players (processors) and m chairs. Initially, players occupy arbitrary chairs. Two players are in conflict if they both occupy the same chair. The task terminates when there are no conflicts and each player occupies a different chair. Our oblivious protocols use only limited communication, and do so in an asynchronous fashion. Essentially, a player can only observe whether the player itself is in conflict or not, and nothing else. A player observing no conflict halts and never changes its chair, whereas a player observing a conflict changes its chair according to its deterministic program. Known results imply that even with more general communication primitives, no strategy of the players can guarantee termination if m < 2n - 1. We show that even with this minimal communication termination can be guaranteed with only m = 2n - 1 chairs. Our oblivious protocol can be extended to the well-known Adaptive Renaming problem, using a name-space that is as small as that of the optimal nonoblivious protocol. We also make substantial progress in optimizing other parameters (such as program length) for our protocols, though many interesting questions remain open.