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Preprints, Working Papers, ...

Mesurer la similarité de graphes

Sébastien Sorlin 1
1 M2DisCo - Geometry Processing and Constrained Optimization
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
Abstract : Many applications such as e.g., information retrieval and classification, involve measuring graph distance or similarity, i.e., matching graphs to identify and quantify their common features. Different kinds of graph matchings have been proposed, giving rise to different graph similarity or distance measures. Exact graph matchings such as graph or subgraph isomorphism can be used in order to show graph equivalence or inclusion. However, in many applications, the assumption of the existence of such an "exact" matching is too strong. As a consequence, error-tolerant graph matchings such as maximum common subgraph and graph edit distance have been proposed. Such matchings drop the condition that the matching must preserve all vertices and edges and look for a "best" matching, i.e., one which preserves a maximum number of vertices and edges. Most recently, three different approaches proposed to go one step further by introducing multivalent matchings where a vertex may be matched with a set of vertices. This kind of matching handles the fact that, due to different description granularity levels, one object component may "play the same role" than a set of components of another object. Un first goal of this work is to define a new graph distance based on the search of a best matching between the graph vertices, i.e., a matching that minimizes vertex and edge distance functions. This distance is generic in the sense that it allows both univalent and multivalent matchings and it is parameterized by vertex and edge distance functions defined by the user depending on the considered application. We show how to use this graph distance generic framework to model existing graph distance or similarity measure. A second goal of this work is to propose an algorithm to compute this generic graph distance. We propose a reactive tabu local search ables to solve many different graph matching problems and give some experimental results. We then focus our attention on solving the graph isomorphism problem with constraint programming. We propose a global constraint dedicated to this problem, a partial consistency for this constraint and an algorithm to establish this consistency. We show that using this consistency makes the constraint programming competitive with algorithms dedicated to this problem.
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Preprints, Working Papers, ...
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Submitted on : Monday, February 13, 2017 - 9:59:44 AM
Last modification on : Tuesday, June 1, 2021 - 2:08:07 PM


  • HAL Id : hal-01465747, version 1


Sébastien Sorlin. Mesurer la similarité de graphes. 2006. ⟨hal-01465747⟩



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