Quasimetric Graph Edit Distance as a Compact Quadratic Assignment Problem

Distance d'édition entre graphes quasimétrique formulée comme un problème compact d'affectation quadratique.

David Blumenthal (1) , Évariste Daller (2) , Sébastien Bougleux (2) , Luc Brun (2) , Johann Gamper (1)

1 unibz - Faculty of Computer Science, Free University of Bozen-Bolzano
2 Equipe Image - Laboratoire GREYC - UMR6072

The graph edit distance (GED) is a widely used distance measure for attributed graphs. It has recently been shown that the problem of computing GED, which is a NP-hard optimization problem, can be formulated as a quadratic assignment problem (QAP). This formulation is useful, since it allows to derive well performing approximative heuristics for GED from existing techniques for QAP. In this paper, we focus on the case where the edit costs that underlie GED are quasimetric. This is the case in many applications of GED. We show that, for quasimetric edit costs, it is possible to reduce the size of the corresponding QAP formulation. An empirical evaluation shows that this reduction significantly speeds up the QAP-based approximative heuristics for GED.

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]

David Blumenthal, Évariste Daller, Sébastien Bougleux, Luc Brun, Johann Gamper. Quasimetric Graph Edit Distance as a Compact Quadratic Assignment Problem. 24th International Conference on Pattern Recognition (ICPR), Aug 2018, Pékin, China. ⟨hal-01865214⟩