Breaking the log n barrier on rumor spreading

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 Ω(logn) is also known for this special case. Under the assumption 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, addressoblivious and robust algorithm that uses push&pull with pointer jumping to spread a rumor to all nodes in only O( √ logn) rounds, w.h.p. This algorithm can also cope with F = O(n/2 √ ) node failures, in which case all but O(F ) nodes become informed within O( √ logn) rounds, w.h.p.