Minimum flow time graph ordering

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. © Springer-Verlag Berlin Heidelberg 2003.