Exact Computation of Graph Edit Distance for Uniform and Non-uniform Metric Edit Costs

  • David B. Blumenthal
  • Johann Gamper
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10310)


The graph edit distance is a well-established and widely used distance measure for labelled, undirected graphs. However, since its exact computation is \( NP \)-hard, research has mainly focused on devising approximative heuristics and only few exact algorithms have been proposed. The standard approach \(\mathtt {A}^\star \)-\(\mathtt {GED}\), a node-based best-first search that works for both uniform and non-uniform metric edit costs, suffers from huge runtime and memory requirements. Recently, two better performing algorithms have been proposed: \(\mathtt {DF}\)-\(\mathtt {GED}\), a node-based depth-first search that works for uniform and non-uniform metric edit costs, and \(\mathtt {CSI\_GED}\), an edge-based depth-first search that works only for uniform edit costs. Our paper contains two contributions: First, we propose a speed-up \(\mathtt {DF}\)-\(\mathtt {GED^{u}}\) of \(\mathtt {DF}\)-\(\mathtt {GED}\) for uniform edit costs. Second, we develop a generalisation \(\mathtt {CSI\_GED^{nu}}\) of \(\mathtt {CSI\_GED}\) that also covers non-uniform metric edit cost. We empirically evaluate the proposed algorithms. The experiments show, i.a., that our speed-up \(\mathtt {DF}\)-\(\mathtt {GED^{u}}\) clearly outperforms \(\mathtt {DF}\)-\(\mathtt {GED}\) and that our generalisation \(\mathtt {CSI\_GED^{nu}}\) is the most versatile algorithm.


Graph matching Graph similarity Graph edit distance Branch and bound 


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Faculty of Computer ScienceFree University of BolzanoBolzanoItaly

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