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Approximability of Connected Factors

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Approximation and Online Algorithms (WAOA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8447))

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Abstract

Finding a d-regular spanning subgraph (or d-factor) of a graph is easy by Tutte’s reduction to the matching problem. By the same reduction, it is easy to find a minimal or maximal d-factor of a graph. However, if we require that the d-factor is connected, these problems become NP-hard – finding a minimal connected 2-factor is just the traveling salesman problem (TSP).

Given a complete graph with edge weights that satisfy the triangle inequality, we consider the problem of finding a minimal connected d-factor. We give a 3-approximation for all d and improve this to an (r + 1)-approximation for even d, where r is the approximation ratio of the TSP. This yields a 2.5-approximation for even d. The same algorithm yields an (r + 1)-approximation for the directed version of the problem, where r is the approximation ratio of the asymmetric TSP. We also show that none of these minimization problems can be approximated better than the corresponding TSP.

Finally, for the decision problem of deciding whether a given graph contains a connected d-factor, we extend known hardness results.

A full version with all proofs is available at http://arxiv.org/abs/1310.2387

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Author information

Authors and Affiliations

  1. University of Twente, Enschede, The Netherlands

    Kamiel Cornelissen, Ruben Hoeksma & Bodo Manthey

  2. Indian Institute of Technology Madras, Chennai, India

    N. S. Narayanaswamy & C. S. Rahul

Authors
  1. Kamiel Cornelissen
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  2. Ruben Hoeksma
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  3. Bodo Manthey
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  4. N. S. Narayanaswamy
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  5. C. S. Rahul
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Editor information

Editors and Affiliations

  1. Computer Technology Institute and Press “Diophantus” & Department of Computer Engineering and Informatics, University of Patras, 26504, Rio, Greece

    Christos Kaklamanis

  2. University of Pittsburgh, 15260, Pittsburgh, PA, USA

    Kirk Pruhs

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Cornelissen, K., Hoeksma, R., Manthey, B., Narayanaswamy, N.S., Rahul, C.S. (2014). Approximability of Connected Factors. In: Kaklamanis, C., Pruhs, K. (eds) Approximation and Online Algorithms. WAOA 2013. Lecture Notes in Computer Science, vol 8447. Springer, Cham. https://doi.org/10.1007/978-3-319-08001-7_11

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  • DOI: https://doi.org/10.1007/978-3-319-08001-7_11

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08000-0

  • Online ISBN: 978-3-319-08001-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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