On Rerouting Connection Requests in Networks with Shared Bandwidth

In this paper, we address the problem of scheduling the switching of a set of connection requests one after the other from current routing to another pre-determined routing. We propose a model that handles requests using only a constant fraction of the bandwidth of a link, thus generalizing the model proposed in [Coudert, D. and J.-S. Sereni, Characterization of graphs and digraphs with small process number, Research Report 6285, INRIA (2007). URL http://hal.inria.fr/inria-00171083/; Jose, N. and A. Somani, Connection rerouting/network reconfiguration, Design of Reliable Communication Networks (2003), pp. 23–30.] for WDM networks. Our main result is the proof that the problem of deciding whether it exists a scheduling of the rerouting of connection requests without traffic interruption is NP-complete even if requests use the third of the bandwidth of a link. Note that the problem is polynomial when the bandwidth of a link cannot be shared [Coudert, D. and J.-S. Sereni, Characterization of graphs and digraphs with small process number, Research Report 6285, INRIA (2007). URL http://hal.inria.fr/inria-00171083/].