## 00-27

#### Unit-Time Job-Shop Scheduling via mixed graph coloring

by Sotskov, Y.N.; Dolgui, A.; Werner, F.

**Preprint series:** 00-27, Preprints

**The paper is published:** International Journal of Mathematical Algorithms, Vol. 2, 2001, 289 -- 323.

**Abstract:** A unit-time scheduling problem with makespan criterion may be interpreted as an optimal coloring of the vertices of a mixed graph, where the number of colors is minimal. We consider an optimal coloring which defines a schedule that minimizes the makespan for a unit-time job-shop problem, present complexity results for some special cases and improve a geometrical algorithm. For the general case, we develop three branch-and-bound algorithms and test them on randomly generated mixed graphs of order $n \leq 200$ for the exact solution and of order $n \leq 900$ for the approximate solution, where $n$ is the number of vertices.

**Keywords:** Scheduling algorithm; Mixed graph; Coloring

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