Summary: Oblivious Collaboration
Eli Gafni §
Nati Linial ¶
March 30, 2011
Communication is a crucial ingredient in every kind of collaborative work. But what is the
least possible amount of communication required for a given task? We formalize this question by
introducing a new framework for distributed computation, called oblivious protocols.
We investigate the power of this model by considering two concrete examples, the musical
chairs task MC(n, m) and the well-known Renaming problem. The MC(n, m) game is played by n
players (processors) with m chairs. Players can occupy chairs, and the game terminates as soon as
each player occupies a unique chair. Thus we say that player P is in conflict if some other player
Q is occupying the same chair, i.e., termination means there are no conflicts. By known results
from distributed computing, if m 2n - 2, no strategy of the players can guarantee termination.
However, there is a protocol with m = 2n - 1 chairs that always terminates. Here we consider
an oblivious protocol where in every time step the only communication is this: an adversarial
scheduler chooses an arbitrary nonempty set of players, and for each of them provides only one bit