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Fixed-Parameter Complexity of Minimum Profile Problems

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Abstract

The profile of a graph is an integer-valued parameter defined via vertex orderings; it is known that the profile of a graph equals the smallest number of edges of an interval supergraph. Since computing the profile of a graph is an NP-hard problem, we consider parameterized versions of the problem. Namely, we study the problem of deciding whether the profile of a connected graph of order n is at most n−1+k, considering k as the parameter; this is a parameterization above guaranteed value, since n−1 is a tight lower bound for the profile. We present two fixed-parameter algorithms for this problem. The first algorithm is based on a forbidden subgraph characterization of interval graphs. The second algorithm is based on two simple kernelization rules which allow us to produce a kernel with linear number of vertices and edges. For showing the correctness of the second algorithm we need to establish structural properties of graphs with small profile which are of independent interest.

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Authors and Affiliations

  1. Department of Computer Science, Royal Holloway University of London, Egham, Surrey TW20 0EX, UK

    Gregory Gutin & Anders Yeo

  2. Department of Computer Science, University of Haifa, Haifa, Israel

    Gregory Gutin

  3. Department of Computer Science, Durham University, Durham, DH1 3LE, UK

    Stefan Szeider

Authors
  1. Gregory Gutin
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  2. Stefan Szeider
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  3. Anders Yeo
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Corresponding author

Correspondence to Gregory Gutin.

Additional information

A preliminary version of the paper is published in Proc. IWPEC 2006, LNCS vol. 4169, 60–71.

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Gutin, G., Szeider, S. & Yeo, A. Fixed-Parameter Complexity of Minimum Profile Problems. Algorithmica 52, 133–152 (2008). https://doi.org/10.1007/s00453-007-9144-0

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  • DOI: https://doi.org/10.1007/s00453-007-9144-0

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