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On Eulerian Extension Problems and their Application to Sequencing Problems
Wiebke Höhn  (TU Berlin)
We introduce a technique for solving several sequencing problems. We consider Gilmore and Gomory's variant of the Traveling Salesman Problem and two variants of no-wait ﬂowshop scheduling, the classical makespan minimization problem and a new problem arising in the multistage production process in steel manufacturing. Our technique is based on an intuitive interpretation of sequencing problems as Eulerian Extension Problems: Given some directed (multi-) graph, one aims at finding minimum cost set of additional arcs such that the resulting graph is Eulerian. This interpretation reveals new structural insights and leads to elegant and simple algorithms and proofs for this ancient type of problems. As a major effect, we compute not only a single solution; instead, we represent the entire space of optimal solutions. For the new ﬂowshop scheduling problem we give a full complexity classiﬁcation for any machine conﬁguration.
This is joint work with Tobias Jacobs (National Institute of
Informatics, Tokyo) and Nicole Megow (MPII, Saarbrücken).
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