Complexity results on a paint shop problem

Authors:
Th. Epping;W. Hochstättler;P. Oertel
Affiliations:
Department of Mathematics, BTU Cottbus, Cottbus, Germany;Department of Mathematics, BTU Cottbus, Cottbus, Germany;Ford Werke AG, Cologne, Germany
Venue:
Discrete Applied Mathematics - The 1st cologne-twente workshop on graphs and combinatorial optimization (CTW 2001)
Year:
2004

Citing 2
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Complexity results on restricted instances of a paint shop problem for words

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Paintshop, odd cycles and necklace splitting

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Complexity results on restricted instances of a paint shop problem for words

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Some heuristics for the binary paint shop problem and their expected number of colour changes

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Abstract

Motivated by an application in the automobile industry, we present results and conjectures on a new combinatorial problem: Given a word w and restricted reservoirs of colored letters, synthesize w with a minimal number of color changes. We present a dynamic program that solves this problem and runs in polynomial time if we bound both, the number of different letters and colors. Otherwise, the problem is shown to be NP-complete. Additionally, we focus on upper bounds on the minimal number of color changes, simultaneously giving results for special instances, and posing open questions.