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(log n) 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, address-oblivious 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/2logn) node failures, in which case all but O(F) nodes become informed within O(logn) rounds, w.h.p.