 
Summary: Oblivious Collaboration
Yehuda Afek
Yakov Babichenko
Uriel Feige
Eli Gafni §
Nati Linial ¶
Benny Sudakov
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 wellknown 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
