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Approximation Algorithms for Connected Maximum Cut and Related Problems

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Algorithms - ESA 2015

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9294))

Abstract

An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V,E) and the goal is to find a subset of vertices S ⊆ V that maximizes the number of edges in the cut δ(S) such that the induced graph G[S] is connected. We present the first non-trivial \(\Omega(\frac{1}{\log n})\) approximation algorithm for the connected maximum cut problem in general graphs using novel techniques. We then extend our algorithm to an edge weighted case and obtain a poly-logarithmic approximation algorithm. Interestingly, in stark contrast to the classical max-cut problem, we show that the connected maximum cut problem remains NP-hard even on unweighted, planar graphs. On the positive side, we obtain a polynomial time approximation scheme for the connected maximum cut problem on planar graphs and more generally on graphs with bounded genus.

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Author information

Authors and Affiliations

  1. University of Maryland, College Park, MD, 20742, USA

    Mohammad Taghi Hajiaghayi & Manish Purohit

  2. Rutgers University - Camden, Camden, NJ, 08102, USA

    Guy Kortsarz & Robert MacDavid

  3. IBM T. J. Watson Research Center, Yorktown Heights, NY, 10598, USA

    Kanthi Sarpatwar

Authors
  1. Mohammad Taghi Hajiaghayi
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  2. Guy Kortsarz
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  3. Robert MacDavid
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  4. Manish Purohit
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  5. Kanthi Sarpatwar
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Corresponding author

Correspondence to Mohammad Taghi Hajiaghayi .

Editor information

Editors and Affiliations

  1. University of Technology, Eindhoven, The Netherlands

    Nikhil Bansal

  2. Sapienza University of Rome, Rome, Italy

    Irene Finocchi

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Hajiaghayi, M.T., Kortsarz, G., MacDavid, R., Purohit, M., Sarpatwar, K. (2015). Approximation Algorithms for Connected Maximum Cut and Related Problems. In: Bansal, N., Finocchi, I. (eds) Algorithms - ESA 2015. Lecture Notes in Computer Science(), vol 9294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48350-3_58

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  • DOI: https://doi.org/10.1007/978-3-662-48350-3_58

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48349-7

  • Online ISBN: 978-3-662-48350-3

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