Complexity results on a paint shop problem Original Research Article

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.