Rumor Spreading with No Dependence on Conductance

In this paper, we study how a collection of interconnected nodes can efficiently perform a global computation in the $\mathcal{GOSSIP}$ model of communication. In this model nodes do not know the global topology of the network and may only initiate contact with a single neighbor in each round. This contrasts with the much less restrictive $\mathcal{LOCAL}$ model, where a node may simultaneously communicate with all of its neighbors in a single round. A basic question in this setting is how many rounds of communication are required for the information dissemination problem, in which each node has some piece of information and is required to collect all others. In the $\mathcal{LOCAL}$ model this is quite simple: each node broadcasts all of its information in each round, and the number of rounds required will be equal to the diameter of the underlying communication graph. In the $\mathcal{GOSSIP}$ model, each node must independently choose a single neighbor to contact, and the lack of global information mak...

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