Improving the Distance Accuracy of Bipartite Graph Edit Distance

Abstract

One of the major problems of the approximation framework BP-GED (presented in the previous chapter) is that it over- or underestimates the true edit distance quite often. This chapter is concerned with two recent extensions of BP-GED that aim at making the distance approximation more accurate. The first idea is based on a post-processing search procedure. That is, rather than directly returning the approximate edit distance $d_{ \psi }(g_1,g_2)$, a search procedure taking the initial assignment $\psi$ as the starting point is carried out. The second strategy for reducing the approximation error of BP-GED is to take more structural information into account when the basic assignment problem is solved on the local substructures of the graphs. To this end, various node centrality measures, originally developed in the context of network analysis, have been adopted by the matching process of BP-GED. These two lines of research are reviewed and evaluated in the present chapter (in Sects. 4.2 and 4.3, respectively).