Error-tolerant graph matching in linear computational cost using an initial small partial matching

Error-tolerant graph matching has been demonstrated to be an NP-problem, therefore, its exact computation has an exponential computational cost and several sub-optimal algorithms have been presented with the aim of making the runtime acceptable in some applications. Some well-known sub-optimal algorithms have sixth, cubic or quadratic computational costs with respect to the order of the graphs. Although these computational costs could be considered very low, when applications deal with large graphs (for instance in social networks), the quadratic cost continues to be unacceptable. For this reason, we present an error-tolerant graph-matching algorithm that has a O(d(3.5) .) computational cost, d being the number of output edges per node and n the order of the graphs. Note that, usually, in social networks, it holds that d << n and for this reason we consider the cost to be linear, in other words O(k .), k being a low constant. Our method needs an initial seed, which is composed of one or several node-to-node mappings. The algorithm has been applied to analyse the evolution of social networks. (C) 2018 Elsevier B.V. All rights reserved.