Optimal Shielding to Guarantee Region-Based Connectivity under Geographical Failures

As networks and their inter-connectivity grow and become complex, failures in the networks impact society and industries more than ever. In these networks the notion of connectedness is the key to understanding and reasoning about these failures. Traditional studies in improving edge/node connectivity assume that failures occur at random. However, in many scenarios (such as earthquakes, hurricanes, and human-designed attacks on networks) failures are not random, and most traditional methods do not always work. To address this limitation, we consider region-based connectivity to capture the local nature of failures under the geographical failure model, where failures may happen only on edges in a sub-network (region) and we want to shield some edges in regions to protect the connectivity. There may be several regions and in different regions the failures occur independently. Firstly, we establish the NP-hardness of the problem for regions, answering a question proposed in previous papers. Secondly, we propose a polynomial-time algorithm for the special case of two regions based on the matroid techniques. Furthermore, we design an ILP-based algorithm to solve the problem for regions. Experimental results on random and real networks show that our algorithms are much faster than previously known algorithms.