Brief Announcement: Optimal Address-Oblivious Epidemic Dissemination

We consider the problem of reliable gossip/epidemic dissemination in a network of n processes using push and pull algorithms. We generalize the random phone call model so that processes can refuse to push a rumor or answer pull requests. With this relaxation, we show that it is possible to disseminate a rumor to all processes with high probability using Theta(ln n) rounds of communication and only n+O(n / ln n) messages, both of which are optimal and achievable with push-pull and pull-only algorithms. Our algorithms are strikingly simple, address-oblivious and thus fully distributed. This contradicts a well-known result of Karp et al. stating that any address-oblivious algorithm requires Omega(n ln ln n) messages. We also develop precise estimates of the number of rounds required in the push and pull phases of our algorithms to guarantee dissemination to all processes with a certain probability. For the push phase, we focus on a practical infect upon contagion approach that balances the load evenly across all processes. As an example, our push-pull algorithm requires 17 rounds to disseminate a rumor to all processes with probability 1 - 10^-100 in a network of one million processes with a communication overhead of only 0.4%.