On the complexity of submap isomorphism and maximum common submap problems - Informatique, Biologie Intégrative et Systèmes Complexes Accéder directement au contenu
Article Dans Une Revue Pattern Recognition Année : 2015

On the complexity of submap isomorphism and maximum common submap problems

Résumé

Generalized maps describe the subdivision of objects in cells and are widely used to model 2D and 3D images. In this context, several pattern recognition tasks involve solving submap isomorphism problems (to decide if a map is included in another map) or, more generally, computing maximum common submaps (to measure the distance between two maps). Recently, we have described a polynomial-time algorithm for solving the submap isomorphism problem when the pattern map is connected. In this paper, we show that submap isomorphism is NP-complete when the pattern map is not connected. Then, we characterize the inherent difficulty of submap isomorphism with respect to the number of connected components. We show that it is Fixed-Parameter Tractable (FPT) and we give an FPT algorithm for submap isomorphism. We experimentally compare this algorithm with a state-of-the-art subgraph isomorphism algorithm for searching for patterns in an image and we show that it is both more accurate and more efficient. Finally, we study the complexity of the maximum common submap problem, and we show that it is NP-hard even though we restrict the problem to the search of common connected submaps.
Fichier principal
Vignette du fichier
article.pdf (596.59 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01022418 , version 1 (20-03-2015)

Identifiants

Citer

Christine Solnon, Guillaume Damiand, Colin de La Higuera, Jean-Christophe Janodet. On the complexity of submap isomorphism and maximum common submap problems. Pattern Recognition, 2015, 48 (2), pp.302--316. ⟨10.1016/j.patcog.2014.05.019⟩. ⟨hal-01022418⟩
668 Consultations
302 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More