G.2.1 Combinatorics (F.2.2)
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Institute
All-optical telecommunication networks allow for switching connections by lightpaths which can pass several network links without any opto-electronic conversion. Upon arrival of a connection request, it must be decided online, i.e., without knowledge of future requests, if it is accepted and in that case on which lightpaths the connection is routed. This online problem with the goal of maximizing the total profit gained by accepted requests is called Dynamic Singleclass Call Admission Problem (DSCA). We present existing and new algorithms for the DSCA as well as their theoretical and practical evaluation.
In the dial-a-ride-problem (DARP) objects have to be moved between given sources and destinations in a transportation network by means of a server. The goal is to find a shortest transportation for the server. We study the DARP when the underlying transportation network forms a caterpillar. This special case is strongly NP-hard in the worst case. We prove that in a probabilistic setting there exists a polynomial time algorithm which almost surely finds an optimal solution. Moreover, with high probability the optimality of the solution found can be certified efficiently. We also examine the complexity of the DARP in a semi-random setting and in the unweighted case.