a sqrt(n/g) method for generating communication sets

In the fully meshed network, where every node is connected directly to every other node, network traffic is very high because in the fully meshed network, number of communication links is $\frac{N\times (N-1)}{2}$ and communication cost is $2\times N\times (N-1)$, where $N$ is total number of nodes in the network. To minimize network traffic, we propose an algorithm for generation of communication sets that allows any two nodes to communicate by traversing at most two nodes regardless of the network size by dividing the nodes in the system into subgroups of size $G$ where $G\ge 1$, which are then organized into quorum groups of size $k_{1} = \left(\sqrt{\frac{N}{G} \, } approx.\right)$ in a method similar to that used in Maekawa's algorithm except that now quorum groups are constructed out of subgroups instead of nodes. The performance analysis of the proposed partitioning algorithm shows that it significantly reduces network traffic as well as total number of communication links required for a node to communicate with other nodes in the system.