Fast gossiping by short messages in rectangular grids

Abstract

Gossiping in a graph is the process of distributing every vertex`s unique information to every other vertex. This thesis deals with the problem of gossiping in rectangular grids under a condition that each communicating vertex can give one packet to only one adjacent vertex and receive one packet from that. For m × n rectangular grids, previous gossiping algorithm takes μ + $\frac{1}{4}mn$ + 2) rounds[5], and known lower bound is μ + 1) [3]. A difficulty of gossiping in m × n rectangular grids is due to the absence of a Hamiltonian cycle where mn is odd. Though they have not a Hamiltonian cycle, they work like a Hamiltonian cycle in our gossiping algorithm. Our gossiping algorithm takes (mn + 9) rounds in m × n grids where mn is odd.