Gossip protocol on the ad hoc networks and its approximated saturation

Percolation theory attracts much attention as theory that can be applied to describe the connectivity of, for example, people or computers. One of the important purposes of percolation theory is to determine the critical probability, but the analytical value of the critical probability is known only for a few typical network graphs. In this paper, we show that the critical probability of site percolation on the square lattice and the critical probability of gossip protocol on the square lattice is equivalent. Furthermore, we evaluate the critical probability by approximating the saturation of gossip protocol.