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The goal of this paper is to explore and to provide tools for the investigation of the problems of unit-length scheduling of incompatible jobs on uniform machines. We present two new algorithms that are a significant improvement over the known algorithms. The first one is Algorithm 2 which is 2-approximate for the problem Qm|pj  = 1, G = bisubquartic|Cmax. The second one is Algorithm 3 which is 4-approximate for the problem Qm|pj  = 1, G = bisubquartic|ΣCj, where m ∈ {2, 3, 4}. The theory behind the proposed algorithms is based on the properties of 2-coloring with maximal coloring width, and on the properties of ideal machine, an abstract machine that we introduce in this paper.
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