Complexity results on a paint shop problem
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
Paintshop, odd cycles and necklace splitting
Discrete Applied Mathematics
Greedy colorings for the binary paintshop problem
Journal of Discrete Algorithms
Complexity results on restricted instances of a paint shop problem for words
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
Some heuristics for the binary paint shop problem and their expected number of colour changes
Journal of Discrete Algorithms
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In the Binary Paint Shop Problem proposed by Epping et al. (2004) [4] one has to find a 0/1-coloring of the letters of a word in which every letter from some alphabet appears twice, such that the two occurrences of each letter are colored differently and the total number of color changes is minimized. Meunier and Sebo (2009) [5] and Amini et al. (2010) [1] gave sufficient conditions for the optimality of a natural greedy algorithm for this problem. Our result is a best possible generalization of their results. We prove that the greedy algorithm optimally colors every suitable subword of a given instance word w if and only if w contains none of the three words (a,b,a,c,c,b), (a,d,d,b,c,c,a,b), and (a,d,d,c,b,c,a,b) as a subword. Furthermore, we relate this to the fact that every member of a family of hypergraphs associated with w is evenly laminar.