Bit complexity of breaking and achieving symmetry in chains and rings

We consider a failure-free, asynchronous message passing network with n links, where the processors are arranged on a ring or a chain. The processors are identically programmed but have distinct identities, taken from {0, 1, . . . , M - 1}. We investigate the communication costs of three well studied tasks: Consensus, Leader, and MaxF (finding the maximum identity). We show that in chain and ring topologies, the message complexities of all three tasks are the same. Hence, we study a finer measure of complexity: the number of transmitted bits required to solve a task T, denoted BitC(T). We prove several new lower bounds (and some simple upper bounds) that imply the following results: For the two processors case, BitC(Consensus) = 2 and BitC(Leader) = BitC(MaxF) = 2 log2 M

• Type: Journal
• Year: 2008
• Where: JACM
• Authors: Yefim Dinitz, Shlomo Moran, Sergio Rajsbaum
• Keywords: Asynchronous Message, Communication Costs, JACM 2008, Processors