Performance and scalability Appraisal of four Directed Weighted Graph Matching Algorithms: A Survey

We conduct an experimental study of four algorithms for the Weighted Graph Matching Problem (WGMP) for directed graphs. The first algorithm is based on Umeyama's Eigen-decomposition approach and provides nearly an optimum solution by means of Hermitian matrices deduced from the adjacency matrices of pairs of directed weighted graphs. The second algorithm is based on Almohamad's Symmetric ploynomial transform approach. The Symmetric polynomial transform is applied to map input data representing polynomial roots into a set of coefficients that are invariant under permutation of the roots. Assuming this transformation, the weights of two nodes can be compared one to one via their resulted invariant coefficients. The third algorithm is inspired from Almohamad's Linear programming approach where the WGMP is initially formulated in a non linear problem and then transformed into a Linear one formulated in L-1 norm. In the two first algorithms, the optimum match is given by the Hungarian method when a permutation exists between each two nodes. The fourth algorithm is an improved version of the first one that gives exact results only for graphs satisfying certain conditions.