Frank Dehne, Roberto Solis-Oba, Jörg-Rüdiger Sack
1 Department of Mathematics and Computer Science (IMADA), Faculty of Science, SDU 2 Computer Science, Department of Mathematics and Computer Science (IMADA), Faculty of Science, SDU 3 University Library of Southern Denmark, SDU 4 Max Planck Institute für Informatik 5 Plantepatologi og Entomologi 6 Department of Mathematics and Computer Science (IMADA), Faculty of Science, SDU
We introduce a variation of the graph isomorphism problem, where, given two graphs G = (V,E) and G = (V,E) and three integers l, d, and k, we seek for a set ⊆ V and a one-to-one mapping f:V → V such that |D| ≤ k and for every vertex v ∈ V \ D and every vertex u ∈ N (v) \ D we have f(u) ∈ N (f(v)). Here, for a graph G and a vertex v, we use N(v) to denote the set of vertices which have distance at most i to v in G. We call this problem Neighborhood-Preserving Mapping (NPM). The main result of this paper is a complete dichotomy of the classical complexity of NPM on trees with respect to different values of l,d,k. Additionally, we present two dynamic programming algorithms for the case that one of the input trees is a path. © 2013 Springer-Verlag.
Lecture Notes in Computer Science: 13th International Symposium, Wads 2013, 2013, p. 427-438
Main Research Area:
Lecture Notes in Computer Science
Algorithms & Data Structures Symposium, 2013