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Neighborhood-Preserving Mapping between Trees

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Algorithms and Data Structures (WADS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8037))

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We introduce a variation of the graph isomorphism problem, where, given two graphs G 1 = (V 1,E 1) and G 2 = (V 2,E 2) and three integers l, d, and k, we seek for a set D ⊆ V 1 and a one-to-one mapping f:V 1 → V 2 such that |D| ≤ k and for every vertex v ∈ V 1 ∖ 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.

Partially supported by the DFG Cluster of Excellence MMCI and the International Max Planck Research School.

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  1. Heath, A.P., Kavraki, L.E.: Computational challenges in systems biology. Computer Science Review 3, 1–17 (2009)

    Article  Google Scholar 

  2. Bunke, H., Riesen, K.: Recent advances in graph-based pattern recognition with applications in document analysis. Pattern Recognition 44, 1057–1067 (2011)

    Article  MATH  Google Scholar 

  3. Riesen, K., Bunke, H.: Approximate graph edit distance computation by means of bipartite graph matching. Image and Vision Computing 27, 950–959 (2009)

    Article  Google Scholar 

  4. Akutsu, T., Fukagawa, D., Halldórsson, M.M., Takasu, A., Tanaka, K.: Approximation and parameterized algorithms for common subtrees and edit distance between unordered trees. Theor. Comput. Sci. 470, 10–22 (2013)

    Article  MATH  Google Scholar 

  5. Akutsu, T., Fukagawa, D., Takasu, A., Tamura, T.: Exact algorithms for computing the tree edit distance between unordered trees. Theor. Comput. Sci. 412, 352–364 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bille, P.: A survey on tree edit distance and related problems. Theor. Comput. Sci. 337, 217–239 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lozano, A., Pinter, R.Y., Rokhlenko, O., Valiente, G., Ziv-Ukelson, M.: Seeded tree alignment. IEEE/ACM Transactions on Computational Biology and Bioinformatics 5, 503–513 (2008)

    Article  Google Scholar 

  8. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman (1979)

    Google Scholar 

  9. Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms, 1st edn. Addison-Wesley Longman Publishing Co., Inc., Boston (1974)

    MATH  Google Scholar 

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Baumbach, J., Guo, J., Ibragimov, R. (2013). Neighborhood-Preserving Mapping between Trees. In: Dehne, F., Solis-Oba, R., Sack, JR. (eds) Algorithms and Data Structures. WADS 2013. Lecture Notes in Computer Science, vol 8037. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40103-9

  • Online ISBN: 978-3-642-40104-6

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