Abstract
Graph based pattern representation offers a number of useful properties. In particular, graphs can adapt their size and complexity to the actual pattern, and moreover, graphs are able to describe structural relations that might exist within a pattern. Yet, the high representational power and flexibility of graphs is accompanied by a significant increase of the complexity of many algorithms. For instance, exact computation of pairwise graph distance can be accomplished in exponential time complexity only. A previously introduced approximation framework reduces the problem of graph distance computation to an instance of a linear sum assignment problem. This allows suboptimal graph distance computation in cubic time. The present paper introduces a novel procedure, which is conceptually related to this previous approach, but offers \(O(n^2 \log (n^2))\) (rather than cubic) run time. We empirically verify the speed up of our novel approximation and show that the faster approximation is able to keep up with the existing framework with respect to distance accuracy.
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Notes
- 1.
Bipartite Graph Edit Distance (LSAPs can be formulated by means of bipartite graphs).
- 2.
The \(i\)-th node \(u_i \in V_1\) is marked as unavailable only, if the corresponding index \(i\) is not equal to \(\varepsilon \), of course. The same accounts for index \(j\) and node \(v_j\in V_2\).
- 3.
Note that both means are computed on the sets of distances where an SMLA approach actually over- or underestimates the original approximation.
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Acknowledgements
This work has been supported by the Hasler Foundation Switzerland and the Swiss National Science Foundation project 200021_153249.
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Riesen, K., Ferrer, M., Bunke, H. (2015). Suboptimal Graph Edit Distance Based on Sorted Local Assignments. In: Schwenker, F., Roli, F., Kittler, J. (eds) Multiple Classifier Systems. MCS 2015. Lecture Notes in Computer Science(), vol 9132. Springer, Cham. https://doi.org/10.1007/978-3-319-20248-8_13
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