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The Approximability of the Binary Paintshop Problem

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2013, RANDOM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8096))

Abstract

In the Binary Paintshop problem, there are m cars appearing in a sequence of length 2m, with each car occurring twice. Each car needs to be colored with two colors. The goal is to choose for each car, which of its occurrences receives either color, so as to minimize the total number of color changes in the sequence. We show that the Binary Paintshop problem is equivalent (up to constant factors) to the Minimum Uncut problem, under randomized reductions. By derandomizing this reduction for hard instances of the Min Uncut problem arising from the Unique Games Conjecture, we show that the Binary Paintshop problem is ω(1)-hard to approximate (assuming the UGC). This answers an open question from [BEH06,MS09,AH11].

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Anupam Gupta

  2. IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY, 10598, USA

    Satyen Kale, Viswanath Nagarajan, Rishi Saket & Baruch Schieber

Authors
  1. Anupam Gupta
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  2. Satyen Kale
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  3. Viswanath Nagarajan
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  4. Rishi Saket
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  5. Baruch Schieber
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Editor information

Editors and Affiliations

  1. University of California, Berkeley, CA, USA

    Prasad Raghavendra

  2. Dept. of computer Science and Engineering, Pennsylvania State University, University Park, PA, USA

    Sofya Raskhodnikova

  3. Institute of Computer Science, University of Kiel, 24118, Kiel, Germany

    Klaus Jansen

  4. University of Geneva, Centre Universitaire d’Informatique, 1227, Carouge, Switzerland

    José D. P. Rolim

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© 2013 Springer-Verlag Berlin Heidelberg

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Gupta, A., Kale, S., Nagarajan, V., Saket, R., Schieber, B. (2013). The Approximability of the Binary Paintshop Problem. In: Raghavendra, P., Raskhodnikova, S., Jansen, K., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2013 2013. Lecture Notes in Computer Science, vol 8096. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40328-6_15

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  • DOI: https://doi.org/10.1007/978-3-642-40328-6_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40327-9

  • Online ISBN: 978-3-642-40328-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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