  We propose a new protocol solving the fundamental problem of disseminating a
piece of information to all members of a group of n players. It builds upon the
classical randomized rumor spreading protocol and several extensions. The main
achievements are the following:
  Our protocol spreads the rumor to all other nodes in the asymptotically
optimal time of (1 + o(1)) \log_2 n. The whole process can be implemented in a
way such that only O(n f(n)) calls are made, where f(n)= \omega(1) can be
arbitrary.
  In contrast to other protocols suggested in the literature, our algorithm
only uses push operations, i.e., only informed nodes take active actions in the
network. To the best of our knowledge, this is the first randomized push
algorithm that achieves an asymptotically optimal running time.

Data Structures and Algorithms;Social and Information Networks