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Decomposition Width of Matroids

  • Daniel Král’
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6198)

Abstract

Hliněný [J. Combin. Theory Ser. B 96 (2006), 325–351] showed that every matroid property expressible in the monadic second order logic can be decided in linear time for matroids with bounded branch-width that are represented over finite fields. To be able to extend these algorithmic results to matroids not representable over finite fields, we introduce a new matroid width parameter, the decomposition width, and show that every matroid property expressible in the monadic second order logic can be computed in linear time for matroids given by a decomposition with bounded width. We also relate the decomposition width to matroid branch-width and discuss implications of our results with respect to other known algorithms.

Keywords

Equivalence Class Order Logic Graph Transformation Parse Tree Width Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Daniel Král’
    • 1
  1. 1.Institute for Theoretical Computer Science (ITI) Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

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