Complexity results on a paint shop problem
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
On the computational complexity of 2-interval pattern matching problems
Theoretical Computer Science
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)
Paintshop, odd cycles and necklace splitting
Discrete Applied Mathematics
Some heuristics for the binary paint shop problem and their expected number of colour changes
Journal of Discrete Algorithms
Computing solutions of the paintshop-necklace problem
Computers and Operations Research
Note: Greedy colorings of words
Discrete Applied Mathematics
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Cars have to be painted in two colors in a sequence where each car occurs twice; assign the two colors to the two occurrences of each car so as to minimize the number of color changes. This problem is denoted by PPW(2,1). This version and a more general version-with an arbitrary multiset of colors for each car-were proposed and studied for the first time in 2004 by Epping, Hochstattler and Oertel. Since then, other results have been obtained: for instance, Meunier and Sebo have found a class of PPW(2,1) instances for which the greedy algorithm is optimal. In the present paper, we focus on PPW(2,1) and find a larger class of instances for which the greedy algorithm is still optimal. Moreover, we show that when one draws uniformly at random an instance w of PPW(2,1), the greedy algorithm needs at most 1/3 of the length of w color changes. We conjecture that asymptotically the true factor is not 1/3 but 1/4. Other open questions are emphasized.