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Space Complexity of Optimization Problems in Planar Graphs

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Theory and Applications of Models of Computation (TAMC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8402))

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Abstract

We initiate the study of space complexity of certain optimization problems restricted to planar graphs. We provide upper bounds and hardness results in space complexity for some of these well-studied problems in the context of planar graphs. In particular we show the following:

1. Max-Cut in planar graphs has a (UL∩co – UL)-approximation scheme;

2. Sparsest-Cut in planar graphs is in NL;

3. Max-Cut in planar graphs is NL-hard;

4. ⊕Directed-Spanning-Trees in planar graphs is ⊕L-complete.

For (1) we analyze the space complexity of the well known Baker’s algorithm [1] using a recent result of Elberfeld, Jakoby, and Tantau [13] that gives a Log-space analogue of Courcelle’s Theorem for MSO definable properties of bounded tree-width graphs.

For (2) we analyze the space complexity of the algorithm of Patel [21] that builds on a useful weighting scheme for planar graphs. Interestingly, the same weighting scheme has been crucially used in the totally different context of isolation in planar graphs [4,7].

For (3) we use a recent result of Kulkarni [17], which shows that Minwt-PM in planar graphs is NL-hard.

For (4) we use the result by Datta, Kulkarni, Limaye, and Mahajan [8] that gives a reduction from the permanent in general graphs to planar graphs.

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Author information

Authors and Affiliations

  1. Chennai Mathematical Institute, India

    Samir Datta

  2. Center for Quantum Technologies, Singapore

    Raghav Kulkarni

Authors
  1. Samir Datta
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  2. Raghav Kulkarni
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, College of Engineering, Anna University, Chennai, 600 025, Chennai, India

    T. V. Gopal

  2. Department of Computer Science and Engineering, Indian Institute of Technology, 208016, Kanpur, India

    Manindra Agrawal

  3. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Zhongguancun, Haidian District, 100190, Beijing, China

    Angsheng Li

  4. School of Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

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Datta, S., Kulkarni, R. (2014). Space Complexity of Optimization Problems in Planar Graphs. In: Gopal, T.V., Agrawal, M., Li, A., Cooper, S.B. (eds) Theory and Applications of Models of Computation. TAMC 2014. Lecture Notes in Computer Science, vol 8402. Springer, Cham. https://doi.org/10.1007/978-3-319-06089-7_21

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  • DOI: https://doi.org/10.1007/978-3-319-06089-7_21

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06088-0

  • Online ISBN: 978-3-319-06089-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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