Abstract
The graph ordering problem here addressed derives from industrial applications where one can associate vertices with process steps and edges with jobs. A linear layout of the vertices corresponds then to a production schedule, and one wants to find a layout minimizing the average completion time of the jobs. We prove that the problem is NP-hard in general and is polynomial on trees. We then provide a 2-approximate algorithm and investigate necessary conditions for optimality. On this basis, we devised a combinatorial branch-and-bound algorithm and tested it on random graphs with up to 100 nodes.
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© 2003 Springer-Verlag Berlin Heidelberg
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Arbib, C., Flammini, M., Marinelli, F. (2003). Minimum Flow Time Graph Ordering. In: Bodlaender, H.L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2003. Lecture Notes in Computer Science, vol 2880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39890-5_3
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DOI: https://doi.org/10.1007/978-3-540-39890-5_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20452-7
Online ISBN: 978-3-540-39890-5
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