TY - GEN A1 - Hiller, Benjamin T1 - Probabilistic Competitive Analysis of a Dial-a-Ride Problem on Trees Under High Load N2 - In this paper we consider a simple variant of the Online Dial-a-Ride Problem from a probabilistic point of view. To this end, we look at a probabilistic version of this online Dial-a-Ride problem and introduce a probabilistic notion of the competitive ratio which states that an algorithm performs well on the vast majority of the instances. Our main result is that under the assumption of high load a certain online algorithm is probabilistically $(1+o(1))$-competitive if the underlying graph is a tree. This result can be extended to general graphs by using well-known approximation techniques at the expense of a distortion factor~$O(\log\|V\|)$. T3 - ZIB-Report - 05-56 KW - probabilistic competitive analysis KW - Dial-a-Ride problem KW - online algorithms KW - IGNORE strategy Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8896 ER - TY - GEN A1 - Hiller, Benjamin A1 - Vredeveld, Tjark T1 - Probabilistic analysis of Online Bin Coloring algorithms via Stochastic Comparison N2 - This paper proposes a new method for probabilistic analysis of online algorithms that is based on the notion of stochastic dominance. We develop the method for the Online Bin Coloring problem introduced by Krumke et al. Using methods for the stochastic comparison of Markov chains we establish the strong result that the performance of the online algorithm GreedyFit is stochastically dominated by the performance of the algorithm OneBin for any number of items processed. This result gives a more realistic picture than competitive analysis and explains the behavior observed in simulations. T3 - ZIB-Report - 08-18 KW - Stochastische Dominanz KW - Online-Algorithmen KW - Markov-Ketten KW - Probabilistische Analyse KW - stochastic dominance KW - online algorithms KW - Markov chains KW - probabilistic analysis Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10726 SN - 1438-0064 ER - 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 -