Fast Suboptimal Algorithms for the Computation of Graph Edit Distance

Abstract

Graph edit distance is one of the most flexible mechanisms for error-tolerant graph matching. Its key advantage is that edit distance is applicable to unconstrained attributed graphs and can be tailored to a wide variety of applications by means of specific edit cost functions. Its computational complexity, however, is exponential in the number of vertices, which means that edit distance is feasible for small graphs only. In this paper, we propose two simple, but effective modifications of a standard edit distance algorithm that allow us to suboptimally compute edit distance in a faster way. In experiments on real data, we demonstrate the resulting speedup and show that classification accuracy is mostly not affected. The suboptimality of our methods mainly results in larger inter-class distances, while intra-class distances remain low, which makes the proposed methods very well applicable to distance-based graph classification.

A graph-based approach for the retrieval of multi-modality medical images

“…Two adaptations of the A algorithm were proposed in [187]. The path length A approach introduces an additional weighting to the A algorithms optimal path and heuristic cost functions to avoid expanding the search tree when a node with a significantly large cost is encountered during vertex mapping.…”

“…The beam search A algorithm approach [187] generates a smaller set of sequences demonstrated that the beam search approach was almost as accurate as a brute force approach when using large beams [187]. When applied to a classification task, the suboptimality of the algorithm resulted in an increase in inter-class differences while intra-class differences were not strongly affected, demonstrating that the algorithm was appropriate for ranking objects images based on similarity of their classes.…”

“…The number of ROIs in our data sets made brute force approaches impractical. While faster methods are generally less accurate, Neuhaus et al [187] demonstrated that the beam search approach was almost as accurate as a brute force method when using large beams. In addition, they demonstrated that the beam search algorithm was appropriate for ranking objects images based on similarity of their classes because it increased inter-class differences while intra-class differences were not strongly affected.…”

“…We compared graphs by adapting the beam search A algorithm [187], which calculates graph edit distances by applying a beam to the well-established A algorithm [186]. Both the standard brute force approach and its beam search adaptation assume a standard set of vertex features.…”

Graph-Based k-Means Clustering: A Comparison of the Set Median versus the Generalized Median Graph

“…In our case, the set of prototypes is exactly the same set S = {g 1 , g 2 , ..., g n } of training graphs that are used to compute the median graph. We therefore compute the graph edit distance between every pair of graphs in the set S. Since computing the graph edit distance is a NP-complete problem, in this work we have used the suboptimal methods presented in [21,22]. The resulting distances are arranged in a distance matrix.…”