Complexity results on a paint shop problem

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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. © 2003 Elsevier B.V. All rights reserved.

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Epping, T., Hochstättler, W., & Oertel, P. (2004). Complexity results on a paint shop problem. In Discrete Applied Mathematics (Vol. 136, pp. 217–226). https://doi.org/10.1016/S0166-218X(03)00442-6

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