Simple and practically efficient fault-Tolerant 2-hop cover labelings

A labeling scheme is a method to retrieve some global property of a graph by exploiting (in a distributed fashion) the information stored, in the form of (short) labels, at its vertices. A classic question in the area is that of labeling the vertices in order to infer the distance between any pair of them, or alternatively to retrieve a corresponding shortest path. On such purpose, among the various solutions, a 2-hop cover distance/path-reporting labeling scheme is based on the idea of representing the shortest paths in a graph as the concatenation at an intermediate so-called hub vertex of the two shortest paths emanating from the corresponding end vertices. The difficult point here is to find a small-size set of hub vertices covering a shortest path for each pair of vertices in the graph, since in this way the corresponding labeling will be compact, but practical efficient solutions are known in the literature. In this paper, we present a simple and efficient way of enriching this successful scheme in order to make it resilient to the failure of a subset of at most k - 1 edges in the graph, by exploiting the notion of so-called edge-independent spanning trees. Depending on k, we provide different strategies and analyze the corresponding performances. In addition, to assess the practical effectiveness of our method, we provide an experimental evaluation, conducted for the case k = 1. Our data confirms the new method to be really competitive when compared with the performance of the benchmark non-fault-Tolerant scheme, equipped with a point-of-failure rerouting policy.