Mathematics in Computer Science

, Volume 2, Issue 4, pp 653–682 | Cite as

Local Algorithms for the Prime Factorization of Strong Product Graphs

  • Marc Hellmuth
  • Wilfried Imrich
  • Werner Klöckl
  • Peter F. Stadler
Open Access
Article

Abstract.

The practical application of graph prime factorization algorithms is limited in practice by unavoidable noise in the data. A first step towards error-tolerant “approximate” prime factorization, is the development of local approaches that cover the graph by factorizable patches and then use this information to derive global factors. We present here a local, quasi-linear algorithm for the prime factorization of “locally unrefined” graphs with respect to the strong product. To this end we introduce the backbone \(\mathbb{B} (G)\) for a given graph G and show that the neighborhoods of the backbone vertices provide enough information to determine the global prime factors.

Mathematics Subject Classification (2000).

Primary 99Z99 Secondary 00A00 

Keywords.

Strong product graphs local covering backbone S1-condition 

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Marc Hellmuth
    • 1
    • 2
  • Wilfried Imrich
    • 3
  • Werner Klöckl
    • 3
  • Peter F. Stadler
    • 1
    • 2
    • 4
    • 5
    • 6
  1. 1.Bioinformatics Group, Department of Computer Science; and Interdisciplinary Center for BioinformaticsUniversity of LeipzigLeipzigGermany
  2. 2.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  3. 3.Chair of Applied Mathematics, MontanuniversitätLeobenAustria
  4. 4.RNomics Group, Fraunhofer Institut für Zelltherapie und ImmunologieLeipzigGermany
  5. 5.Department of Theoretical ChemistryUniversity of ViennaWienAustria
  6. 6.Santa Fe InstituteSanta FeUSA

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