TY - THES A1 - Hiller, Benjamin T1 - Bad Guys are Rare: Probabilistic Analysis of an Elementary Dial-a-Ride Problem N2 - This thesis deals with a Dial-a-Ride problem on trees and considers both offline and online versions of this problem. We study the behavior of certain algorithms on random instances, i.e. we do probabilistic analysis. The focus is on results describing the typical behavior of the algorithms, i.e. results holding with (asymptotically) high probability. For the offline version, we present a simplified proof of a result of Coja-Oghlan, Krumke und Nierhoff. The results states that some heuristic using a minimum spanning tree to approximate a Steiner tree gives optimal results with high probability. This explains why this heuristic produces optimal solutions quite often. In the second part, probabilistic online versions of the problem are introduced. We study the online strategies REPLAN and IGNORE. Regarding the IGNORE strategy we can show that it works almost optimal under high load with high probability. KW - Dial-a-Ride problem on trees KW - probabilistic analysis KW - online algorithms Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10114 ER - TY - THES A1 - Tuchscherer, Andreas T1 - Dynamical Configuration of Transparent Optical Telecommunication Networks N2 - 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. KW - Online-Optimierung KW - Online Optimization Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10214 ER - TY - GEN A1 - Coja-Oghlan, Amin A1 - Krumke, Sven A1 - Nierhoff, Till T1 - Average Case Analysis of a Hard Dial-a-Ride Problem N2 - 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. T3 - ZIB-Report - 03-12 KW - dial-a-ride-problem KW - average case analysis KW - MST-heuristic KW - Steiner trees KW - NP-hardness Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7348 ER - TY - GEN A1 - Heinz, Stefan A1 - Kaibel, Volker A1 - Peinhardt, Matthias A1 - Rambau, Jörg A1 - Tuchscherer, Andreas T1 - LP-Based Local Approximation for Markov Decision Problems N2 - The standard computational methods for computing the optimal value functions of Markov Decision Problems (MDP) require the exploration of the entire state space. This is practically infeasible for applications with huge numbers of states as they arise, e.\,g., from modeling the decisions in online optimization problems by MDPs. Exploiting column generation techniques, we propose and apply an LP-based method to determine an $\varepsilon$-approximation of the optimal value function at a given state by inspecting only states in a small neighborhood. In the context of online optimization problems, we use these methods in order to evaluate the quality of concrete policies with respect to given initial states. Moreover, the tools can also be used to obtain evidence of the impact of single decisions. This way, they can be utilized in the design of policies. T3 - ZIB-Report - 06-20 KW - Markov decision problem KW - linear programming KW - column generation Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9131 ER -