@misc{Hiller2005, author = {Hiller, Benjamin}, title = {Probabilistic Competitive Analysis of a Dial-a-Ride Problem on Trees Under High Load}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8896}, number = {05-56}, year = {2005}, abstract = {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\|)\$.}, language = {en} } @misc{KrumkeLauraLipmannetal.2002, author = {Krumke, Sven and Laura, Luigi and Lipmann, Maarten and Marchetti-Spaccamela, Alberto and Paepe, Willem de and Poensgen, Diana and Stougie, Leen}, title = {Non-Abusiveness Helps: An O(1)-Competitive Algorithm for Minimizing the Maximum Flow Time in the Online Traveling Salesman Problem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7038}, number = {02-36}, year = {2002}, abstract = {In the online traveling salesman problem \$OLTSP\$ requests for visits to cities arrive online while the salesman is traveling. We study the \$F{\_max}-OLTSP\$ where the objective is to minimize the maximum flow time. This objective is particularly interesting for applications. Unfortunately, there can be no competitive algorithm, neither deterministic nor randomized. Hence, competitive analysis fails to distinguish online algorithms. Not even resource augmentation which is helpful in scheduling works as a remedy. This unsatisfactory situation motivates the search for alternative analysis methods. We introduce a natural restriction on the adversary for the \$F{\_max}-OLTSP\$ on the real line. A \emph{non-abusive adversary} may only move in a direction if there are yet unserved requests on this side. Our main result is an algorithm which achieves a constant competitive ratio against the non-abusive adversary.}, language = {en} } @misc{KrumkePoensgen2002, author = {Krumke, Sven and Poensgen, Diana}, title = {Online Call Admission in Optical Networks with Larger Wavelength Demands}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6890}, number = {02-22}, year = {2002}, abstract = {In the problem of \emph{Online Call Admission in Optical Networks}, briefly called \textsc{oca}, we are given a graph \$G=(V,E)\$ together with a set of wavelengths~\$W\$ and a finite sequence \$\sigma=r_1,r_2,\dots\$ of calls which arrive in an online fashion. Each call~\$r_j\$ specifies a pair of nodes to be connected and an integral demand indicating the number of required lightpaths. A lightpath is a path in~\$G\$ together with a wavelength~\$\lambda \in W\$. Upon arrival of a call, an online algorithm must decide immediately and irrevocably whether to accept or to reject the call without any knowledge of calls which appear later in the sequence. If the call is accepted, the algorithm must provide the requested number of lightpaths to connect the specified nodes. The essential restriction is the wavelength conflict constraint: each wavelength is available only once per edge, which implies that two lightpaths sharing an edge must have different wavelengths. Each accepted call contributes a benefit equal to its demand to the overall profit. The objective in \textsc{oca} is to maximize the overall profit. Competitive algorithms for \textsc{oca} have been known for the special case where every call requests just a single lightpath. In this paper we present the first competitive online algorithms for the general case of larger demands.}, language = {en} } @misc{Krumke2000, author = {Krumke, Sven}, title = {News from the Online Traveling Repairman}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5767}, number = {00-08}, year = {2000}, abstract = {The traveling repairman problem (TRP) is a variant of the famous traveling salesman problem (TSP). The objective for the TRP is to minimize the latency, that is the the weighted sum of completion times of the cities, where the completion time of a city is defined to be the time in the tour before the city is reached. In the online traveling repairman problem (OLTRP) requests for visits to cities (points in a metric space) arrive online while the repairman is traveling. We analyze the performance of algorithms using competitive analysis, where the cost of an online algorithm is compared to that of an optimal offline algorithm. An optimal offline algorithm knows the entire request sequence in advance and can serve it with minimum cost. Recently, Feuerstein and Stougie presented a \$9\$-competitive algorithm for the OLTRP on the real line. In this paper we show how to use techniques from online-scheduling to obtain an \$8\$-competitive deterministic algorithm which works for any metric space. We also present a randomized algorithm which has a competitive ratio of \$\frac{4}{\ln 2}\approx 5.7708\$ against an oblivious adversary. All of our results also hold for the ``dial-a-ride'' generalization of the OLTRP, where objects have to be picked up and delivered by a server.}, language = {en} } @misc{HauptmeierKrumkeRambauetal.1999, author = {Hauptmeier, Dietrich and Krumke, Sven and Rambau, J{\"o}rg and Wirth., Hans-Christoph}, title = {Euler is Standing in Line}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3947}, number = {SC-99-06}, year = {1999}, abstract = {In this paper we study algorithms for ``Dial-a-Ride'' transportation problems. In the basic version of the problem we are given transportation jobs between the vertices of a graph and the goal is to find a shortest transportation that serves all the jobs. This problem is known to be NP-hard even on trees. We consider the extension when precedence relations between the jobs with the same source are given. Our results include a polynomial time algorithm on paths and an approximation algorithm on general graphs with a performance of~\$9/4\$. For trees we improve the performance to~\$5/3\$.}, language = {en} } @misc{KrumkePaepeRambauetal.2001, author = {Krumke, Sven and Paepe, Willem de and Rambau, J{\"o}rg and Stougie, Leen}, title = {Online Bin-Coloring}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6338}, number = {01-07}, year = {2001}, abstract = {We introduce a new problem that was motivated by a (more complicated) problem arising in a robotized assembly enviroment. The bin coloring problem is to pack unit size colored items into bins, such that the maximum number of different colors per bin is minimized. Each bin has size~\$B\in\mathbb{N}\$. The packing process is subject to the constraint that at any moment in time at most \$q\in\mathbb{N}\$ bins may be partially filled. Moreover, bins may only be closed if they are filled completely. An online algorithm must pack each item must be packed without knowledge of any future items. We investigate the existence of competitive online algorithms for the online uniform binpacking problem. We show upper bounds for the bin coloring problem. We prove an upper bound of \$3q\$ - 1 and a lower bound of \$2q\$ for the competitive ratio of a natural greedy-type algorithm, and show that surprisingly a trivial algorithm which uses only one open bin has a strictly better competitive ratio of \$2q\$ - 1. Morever, we show that any deterministic algorithm has a competitive ratio \$\Omega (q)\$ and that randomization does not improve this lower bound even when the adversary is oblivious.}, language = {en} } @phdthesis{Krumke2002, author = {Krumke, Sven}, title = {Online Optimization: Competitive Analysis and Beyond}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6925}, number = {02-25}, year = {2002}, abstract = {Traditional optimization techniques assume, in general, knowledge of all data of a problem instance. There are many cases in practice, however, where decisions have to be made before complete information about the data is available. In fact, it may be necessary to produce a part of the problem solution as soon as a new piece of information becomes known. This is called an \emph{online situation}, and an algorithm is termed \emph{online}, if it makes a decision (computes a partial solution) whenever a new piece of data requests an action. \emph{Competitive analysis} has become a standard yardstick to measure the quality of online algorithms. One compares the solution produced by an online algorithm to that of an optimal (clairvoyant) offline algorithm. An online algorithm is called \$c\$-competitive if on every input the solution it produces has cost'' at most \$c\$~times that of the optimal offline algorithm. This situation can be imagined as a game between an online player and a malicious adversary. Although competitive analysis is a worst-case analysis and henceforth pessimistic, it often allows important insights into the problem structure. One can obtain an idea about what kind of strategies are promising for real-world systems and why. On the other hand there are also cases where the offline adversary is simply too powerful and allows only trivial competitiveness results. This phenomenon is called hitting the triviality barrier''. We investigate several online problems by means of competitive analysis. We also introduce new concepts to overcome the weaknesses of the standard approach and to go beyond the triviality barrier.}, language = {en} }