p-Cycles offer ring-like switching speed and mesh-like spare capacity efficiency for protecting network against link failures. This makes them extremely efficient and effective protection technique. p-Cycles can also protect all the links in a network against simultaneous failures of multiple links. But it has been mostly studied for single link failure scenarios in the networks with the objective to minimize spare capacity under the condition of100% restorability. For large networks, use of p-cycles is difficult because their optimization requires an excessive amount of time as the number of variables in the corresponding Integer Linear Program (ILP) increase with the increase in the network size. In a real-time network situation,setting up a highly efficient protection in a short time is essential.Thus, we introduce a network sub-graphing approach, in which a network is segmented into smaller parts based on certain network attributes. Then, an optimal solution is found for each sub-graph. Finally, the solutions for all the sub-graphs is combined to get a sub-optimal solution for the whole network. We achieved better computational efficiency at the expense of marginal spare capacity increases with this approach.