Neighborhood-Preserving Mapping between Trees

  • Jan Baumbach
  • Jiong Guo
  • Rashid Ibragimov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8037)

Abstract

We introduce a variation of the graph isomorphism problem, where, given two graphs G1 = (V1,E1) and G2 = (V2,E2) and three integers l, d, and k, we seek for a set D ⊆ V1 and a one-to-one mapping f:V1 → V2 such that |D| ≤ k and for every vertex v ∈ V1 ∖ D and every vertex \(u\in N_{G_1}^l(v)\setminus D\) we have \(f(u)\in N_{G_2}^d(f(v))\). Here, for a graph G and a vertex v, we use \(N_{G}^i(v)\) 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.

Keywords

tree edit distance graph algorithms complexity graph matching 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jan Baumbach
    • 1
    • 3
  • Jiong Guo
    • 2
  • Rashid Ibragimov
    • 1
  1. 1.Max Planck Institute für InformatikSaarbrückenGermany
  2. 2.Universität des SaarlandesSaarbrückenGermany
  3. 3.University of Southern DenmarkOdense MDenmark

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