Beyond connectivity - new metrics to evaluate robustness of networks

Robustness or fault-tolerance capability of a network is an important design parameter in both wired and wireless networks. Connectivity of a network is traditionally considered to be the primary metric for evaluation of its fault-tolerance capability. However, connectivity κ(G) (for random faults) or region-based connectivity κ_R(G) (for spatially correlated or region-based faults, where the faults are confined to a region R) of a network G, does not provide any information about the network state, (i.e., whether the network is connected or not) once the number of faults exceeds κ(G) or κ_R(G). If the number of faults exceeds κ(G) or κ_R(G), one would like to know, (i) the number of connected components into which G decomposes, (ii) the size of the largest connected component, (iii) the size of the smallest connected component. In this paper, we introduce a set of new metrics that computes these values. We focus on one particular metric called region-based component decomposition number (RBCDN), that measures the number of connected components in which the network decomposes once all the nodes of a region fail. We study the computational complexity of finding RBCDN of a network. In addition, we study the problem of least cost design of a network with a target value of RBCDN. We show that the optimal design problem is NP-complete and present an approximation algorithm with a performance bound of O(log K + 4log n), where n denotes the number of nodes in the graph and K denotes a target value of RBCDN. We evaluate the performance of our algorithm by comparing it with the performance of the optimal solution. Experimental results demonstrate that our algorithm produces near optimal solution in a fraction of time needed to find an optimal solution.