Region-Based Connectivity - A New Paradigm for Design of Fault-tolerant Networks

The studies in fault-tolerance in networks mostly focus on the connectivity of the graph as the metric of fault-tolerance. If the underlying graph is k-connected, it can tolerate up to k - 1 failures. In measuring the fault tolerance in terms of connectivity, no assumption regarding the locations of the faulty nodes are made - the failed nodes may be close to each other or far from each other. In other words, the connectivity metric has no way of capturing the notion of locality of faults. However in many networks, faults may be highly localized. This is particularly true in military networks, where an enemy bomb may inflict massive but localized damage to the network. To capture the notion of locality of faults in a network, a new metric region-based connectivity (RBC) was introduced in [1]. It was shown that RBC can achieve the same level of fault-tolerance as the metric connectivity, with much lower networking resources. The study in [1] was restricted to single region fault model (SRFM), where faults are confined to one region only. In this paper, we extend the notion of RBC to multiple region fault model (MRFM), where faults are no longer confined to a single region. As faults in MRFM are still confined to regions, albeit multiple of them, it is different from unconstrained fault model where no constraint on locality of faults is imposed. The MRFM leads to several new concepts, such as region-disjoint paths and region cuts. We show that the classical result, the maximum number of node-disjoint paths between a pair of nodes is equal to the minimum number of nodes whose removal disconnects the pair, is no longer valid when region-disjoint paths and region cuts are considered. We prove that the problems of finding (i) the maximum number of region-disjoint paths between a pair of nodes, and (ii) minimum number of regions whose removal disconnect a pair of nodes, are both NP-complete. We provide heuristic solution to these two problems and evaluate their efficacy by comparing the results with optimal solutions.