Graph matching by relaxation technique

In this paper, we describe a hybrid relaxation approach to a graph matching problem, by combining both the discrete and continuous relaxation techniques. Compatibility coefficient, critical factor for both relaxation techniques, is defined in terms of nodes and arcs attributes, and the distance measure between graphs is defined as the inner product of the probability vector and the compatibility vector. The discrete relaxation is used as a preprocessing step to determine the initial matching probabilities, and in the continuous relaxation stage, the final matching probabilities are computed by the gradient projection method, Experimental results show that the proposed algorithm is robust to the corruption of the topologies of the graphs, and the matching probabilities converges very rapidly, alleviating an enormous computational load required for the relaxation process.