The approximability of the binary paintshop problem

Anupam Gupta, Satyen Kale, Viswanath Nagarajan, Rishi Saket, Baruch Schieber

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

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].

Original languageEnglish (US)
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 16th International Workshop, APPROX 2013 and 17th International Workshop, RANDOM 2013, Proceedings
Pages205-217
Number of pages13
DOIs
StatePublished - Oct 15 2013
Externally publishedYes
Event16th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2013 and the 17th International Workshop on Randomization and Computation, RANDOM 2013 - Berkeley, CA, United States
Duration: Aug 21 2013Aug 23 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8096 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference16th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2013 and the 17th International Workshop on Randomization and Computation, RANDOM 2013
CountryUnited States
CityBerkeley, CA
Period8/21/138/23/13

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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