On the complexity of Submap Isomorphism

Christine Solnon (1) , Guillaume Damiand (1) , Colin de La Higuera (2) , Jean-Christophe Janodet (3)

1 M2DisCo - Geometry Processing and Constrained Optimization
2 LINA - Laboratoire d'Informatique de Nantes Atlantique
3 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes

Generalized maps describe the subdivision of objects in cells, and incidence and adjacency relations between cells, and they are widely used to model 2D and 3D images. Recently, we have defined submap isomorphism, which involves deciding if a copy of a pattern map may be found in a target map, and we have described a polynomial time algorithm for solving this problem when the pattern map is connected. In this paper, we show that submap isomorphism becomes NP-complete when the pattern map is not connected, by reducing the NP-complete problem Planar-4 3-SAT to it.

Keywords: NP-complete; Submap isomorphism; complexity; NP-complete.

Domains: Data Structures and Algorithms [cs.DS]; Computational Complexity [cs.CC]

Christine Solnon, Guillaume Damiand, Colin de La Higuera, Jean-Christophe Janodet. On the complexity of Submap Isomorphism. Graph-Based Representation in Pattern Recognition, May 2013, Vienna, Austria. pp.21-30, ⟨10.1007/978-3-642-38221-5_3⟩. ⟨hal-00825794⟩