Section: New Results

Graph matching and median graph through simulating annealing

Participants : Zhankeng Zhang, Xavier Descombes.

Graph matching when the number of nodes and edges differs is known as an NP-hard problem. Therefore, sub-optimal optimization algorithms have been proposed to solve this problem. In this work, we evaluate the possibility to reach, at least theoretically, the global optimum by using simulated annealing. We have developed an improved version of the simulating annealing scheme based on a Metropolis sampler. To solve the problem of dimension matching (different number of nodes) we have classically added dummy nodes in the smaller graph. Besides, we have shown that adding dummy nodes in both graphs provides more flexibility in the matching, thus improving the matching result. Finally, within this framework we were able to define and compute "median" graph as shown on figure 11. The algorithm consists in aligning all the graphs in a first step. The median graph is then obtained by considering two types of move in the simulated annealing: adding/removing an edge and switching two nodes. To validate this work we have considered a classification scheme between graphs. The obtained results overcome those obtained with state of the art graph matching algorithms while the computational time remains reasonable.

Figure 11. Four samples of noisy SUN graph and computed median graph