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Bipartite Graph Edit Distance

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Book cover Structural Pattern Recognition with Graph Edit Distance

Part of the book series: Advances in Computer Vision and Pattern Recognition ((ACVPR))

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Abstract

In this chapter, we reformulate the graph edit distance problem to a quadratic assignment problem. This reformulation actually builds the basis for a recent approximation algorithm, which in turn builds the core algorithm for the second part of the present book. This particular approximation algorithm, which gives rise to an upper and a lower bound of the true edit distance, is thoroughly reviewed in the present chapter (including an empirical evaluation on four standard graph sets). Finally, we give a brief survey of pattern recognition applications that make use of this specific approximation algorithm.

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Notes

  1. 1.

    Alternatively, one could use half of the cost. Formally, \(\frac{1}{2}\sum _{i=1}^{n+m}\sum _{j=1}^{n+m} c (a_{ij} \rightarrow b_{\varphi _i \varphi _j})\).

  2. 2.

    Note the change of notation from \(\lambda \) to \(\psi \). From now on we will use \(\psi \) for explicitly denoting edit paths, which are found by an LSAP solving algorithm on \(\mathbf {C}^*\).

  3. 3.

    For the sake of convenience we regard the undirected case only. That is, for the computation of \(c^*_{i\varphi ^*_i}\) the outgoing edges are considered only. Formally, we make use of Eq. 3.10 instead of Eq. 3.9 (yet, the directed case can be defined analogously).

  4. 4.

    The assignment problem can also be formulated as finding a matching in a complete bipartite graph and is therefore also referred to as bipartite graph matching problem.

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  1. Institut für Wirtschaftsinformatik, Fachhochschule Nordwestschweiz, Olten, Switzerland

    Kaspar Riesen

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Riesen, K. (2015). Bipartite Graph Edit Distance. In: Structural Pattern Recognition with Graph Edit Distance. Advances in Computer Vision and Pattern Recognition. Springer, Cham. https://doi.org/10.1007/978-3-319-27252-8_3

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  • DOI: https://doi.org/10.1007/978-3-319-27252-8_3

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