Complexity results for Weighted Timed Event Graphs

Authors:
Olivier Marchetti;Alix Munier-Kordon
Affiliations:
Laboratoire LIP6, Université Pierre et Marie Curie, 4 place Jussieu, 75 252 Paris, Cedex 05, France;Laboratoire LIP6, Université Pierre et Marie Curie, 4 place Jussieu, 75 252 Paris, Cedex 05, France
Venue:
Discrete Optimization
Year:
2010

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Abstract

The minimization of the amount of initial tokens in a Weighted Timed Event Graph (in short WTEG) or a Timed Event Graph (in short TEG) under throughput constraint is a crucial problem in industrial area such as the design of manufacturing systems or embedded systems. Two important variants are studied in this paper: the first one concerns the maximization of the throughput for minimum places capacities of a TEG. It is proved NP-complete by a polynomial reduction with the K-colorability problem. The second one is the minimization of the overall places capacities with a maximum throughput. This problem is also proved NP-complete for a TEG. A polynomial subcase and a 2-approximation polynomial algorithm for a WTEG are then provided.