Neighborhood-Preserving mapping between trees

  • Authors:

  • Jan Baumbach;Jiong Guo;Rashid Ibragimov

  • Affiliations:

  • Max Planck Institute für Informatik, Saarbrücken, Germany,University of Southern Denmark, Odense M, Denmark;Universität des Saarlandes, Saarbrücken, Germany;Max Planck Institute für Informatik, Saarbrücken, Germany

  • Venue:
  • WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
  • Year:
  • 2013

Quantified Score

Hi-index 0.00

Visualization

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.