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On the Complexity of Partial Order Properties

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Abstract

The recognition complexity of ordered set properties is considered in terms of how many questions must be put to an adversary to decide if an unknown partial order has the prescribed property. We prove a lower bound of order n 2 for properties that are characterized by forbidden substructures of fixed size. For the properties being connected, and having exactly k comparable pairs, k ≤ n 2 / 4 we show that the recognition complexity is (n\choose 2). The complexity of interval orders is exactly (n\choose 2) - 1. We further establish bounds for being a lattice, being of height k and having width k.

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Authors and Affiliations

  1. Institut für Informatik, Fachbereich Mathematik, Freie Universität Berlin, Takustraße 9, 14195, Berlin, Germany

    Stefan Felsner

  2. Dept. of Computer Science and Engineering, Indian Institute of Technology, Madras, India, 600 036

    Ravi Kant & C. Pandu Rangan

  3. Fakultät für Mathematik und Informatik, Universität Konstanz, Fach D 188, 78457, Konstanz, Germany

    Dorothea Wagner

Authors
  1. Stefan Felsner
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  2. Ravi Kant
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  3. C. Pandu Rangan
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  4. Dorothea Wagner
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Felsner, S., Kant, R., Rangan, C.P. et al. On the Complexity of Partial Order Properties. Order 17, 179–193 (2000). https://doi.org/10.1023/A:1006422023869

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  • DOI: https://doi.org/10.1023/A:1006422023869

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