# Faster Rumor Spreading: Breaking the log n Barrier

## Chen Avin and Robert Elsässer

Abstract. $O(\log{n})$ rounds has been a well known upper bound for rumor spreading using push&pull in the random phone call model (i.e., uniform gossip in the complete graph). A matching lower bound of $\Omega(\log{n})$ is also known for this special case. Under the assumptions of this model and with a natural addition that nodes can call a partner once they learn its address (e.g., its IP address) we present a new distributed, address-oblivious and robust algorithm that uses push&pull with pointer jumping to spread a rumor to all nodes in only $O(\sqrt{\log{n}})$ rounds, w.h.p. This algorithm can also cope with $F = o( n/2^{\sqrt{\log{n}}} )$ node failures, in which case all but $O(F)$ nodes become informed within $O(\sqrt{\log{n}})$ rounds, w.h.p.

Guest: Chen Avin

Host: Shantanu Das