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On the complexity of partial order properties

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Graph-Theoretic Concepts in Computer Science (WG 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 657))

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Abstract

The recognition complexity of ordered set properties is considered, i.e. how many questions have to be asked to decide if an unknown ordered set has a prescribed property. We prove a lower bound of Ω(n 2) for properties that are characterized by forbidden substructures of fixed size. For the properties being connected, and having exactly k comparable pairs we show that the recognition complexity is ( n2 ); the complexity of interval orders is exactly ( n2 ) — 1. Non-trivial upper bounds are given for being a lattice, containing a chain of length k ≥ 3 and having width k.

This research was partially supported by the Deutsche Forschungsgemeinschaft under grant Mö 446/1-3.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, W-1000, Berlin 12, Germany

    Stefan Felsner & Dorothea Wagner

Authors
  1. Stefan Felsner
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  2. Dorothea Wagner
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Ernst W. Mayr

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© 1993 Springer-Verlag Berlin Heidelberg

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Felsner, S., Wagner, D. (1993). On the complexity of partial order properties. In: Mayr, E.W. (eds) Graph-Theoretic Concepts in Computer Science. WG 1992. Lecture Notes in Computer Science, vol 657. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56402-0_50

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  • DOI: https://doi.org/10.1007/3-540-56402-0_50

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56402-7

  • Online ISBN: 978-3-540-47554-5

  • eBook Packages: Springer Book Archive

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