The Approximability of the Binary Paintshop Problem

  • Anupam Gupta
  • Satyen Kale
  • Viswanath Nagarajan
  • Rishi Saket
  • Baruch Schieber
Conference paper

DOI: 10.1007/978-3-642-40328-6_15

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8096)
Cite this paper as:
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. Lecture Notes in Computer Science, vol 8096. Springer, Berlin, Heidelberg

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Anupam Gupta
    • 1
  • Satyen Kale
    • 2
  • Viswanath Nagarajan
    • 2
  • Rishi Saket
    • 2
  • Baruch Schieber
    • 2
  1. 1.Dept. of Computer ScienceCarnegie Mellon UniversityPittsburghUSA
  2. 2.IBM T.J. Watson Research CenterYorktown HeightsUSA

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