@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{GroetschelKrumkeRambauetal.2002, author = {Gr{\"o}tschel, Martin and Krumke, Sven and Rambau, J{\"o}rg and Torres, Luis Miguel}, title = {Making the Yellow Angels Fly: Online Dispatching Of Service Vehicles in Real Time}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6858}, number = {02-18}, year = {2002}, abstract = {Combinatorial online optimization is an area with lots of applications and potential for significant progress, both in theory and practice. In this short note we sketch the ADACproblem, a typical large-scale online optimization problem, discuss some theoretical and pratical issues coming up, and explain, very briefly, how we approach this problem mathematically. Online problems are a battlefield of heuristics with many strong claims about their solution quality. We indicate that a stronger problem orientation and the use of a little more mathematics may yield.}, 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{KrumkeLipmannPaepeetal.2002, author = {Krumke, Sven and Lipmann, Maarten and Paepe, Willem de and Poensgen, Diana and Rambau, J{\"o}rg and Stougie, Leen and Woeginger, Gerhard}, title = {How to Cut a Cake Almost Fairly}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6905}, number = {02-23}, year = {2002}, abstract = {In the cake cutting problem, \$n\ge2\$ players want to cut a cake into \$n\$ pieces so that every player gets a ``fair'' share of the cake by his own measure. We describe a protocol with \$n-1\$~cuts in which each player can enforce to get a share of at least~\$1/(2n-2)\$. Moreover we show that no protocol with \$n-1\$~cuts can guarantee a better fraction.}, language = {en} } @misc{KrumkeMarathePoensgenetal.2002, author = {Krumke, Sven and Marathe, Madhav and Poensgen, Diana and Ravi, Sekharipuram S. and Wirth, Hans-Christoph}, title = {Budgeted Maximal Graph Coverage}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6918}, number = {02-24}, year = {2002}, abstract = {An instance of the \emph{maximum coverage} problem is given by a set of weighted ground elements and a cost weighted family of subsets of the ground element set. The goal is to select a subfamily of total cost of at most that of a given budget maximizing the weight of the covered elements. We formulate the problem on graphs: In this situation the set of ground elements is specified by the nodes of a graph, while the family of covering sets is restricted to connected subgraphs. We show that on general graphs the problem is polynomial time solvable if restricted to sets of size at most~\$2\$, but becomes NP-hard if sets of size~\$3\$ are permitted. On trees, we prove polynomial time solvability if each node appears in a fixed number of sets. In contrast, if vertices are allowed to appear an unbounded number of times, the problem is NP-hard even on stars. We finally give polynomial time algorithms for special cases where the subgraphs form paths and the host graph is a line, a cycle or a star.}, 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{BlomKrumkePaepeetal.2000, author = {Blom, Michiel and Krumke, Sven and Paepe, Willem de and Stougie, Leen}, title = {The Online-TSP Against Fair Adversaries}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5779}, number = {00-09}, year = {2000}, abstract = {In the online traveling salesman problem requests for visits to cities (points in a metric space) arrive online while the salesman is traveling. The salesman moves at no more than unit speed and starts and ends his work at a designated origin. The objective is to find a routing for the salesman which finishes as early as possible. Performance of algorithms is measured through their competitive ratio, comparing the outcome of the algorithms with that of an adversary who provides the problem instance and therefore is able to achieve the optimal offline solution. Objections against such omnipotent adversaries have lead us to devise an adversary that is in a natural way, in the context of routing problems, more restricted in power. For the exposition we consider the online traveling salesman problem on the metric space given by the non-negative part of the real line. We show that a very natural strategy is~\$3/2\$-competitive against the conventional adversary, which matches the lower bound on competitive ratios achievable for algorithms for this problem. Against the more ``\emph{fair adversary}'', that we propose, we show that there exists an algorithm with competitive ratio \$\frac{1+\sqrt{17}}{4}\approx 1.28\$ and provide a matching lower bound. We also show competitiveness results for a special class of algorithms (called zealous algorithms) that do not allow waiting time for the server as long as there are requests unserved.}, language = {en} } @misc{KonjevodKrumkeMarathe2000, author = {Konjevod, Goran and Krumke, Sven and Marathe, Madhav}, title = {Budget Constrained Minimum Cost Connected Medians}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5783}, number = {00-10}, year = {2000}, abstract = {Several practical instances of network design problems require the network to satisfy multiple constraints. In this paper, we address the \emph{Budget Constrained Connected Median Problem}: We are given an undirected graph \$G = (V,E)\$ with two different edge-weight functions \$c\$ (modeling the construction or communication cost) and \$d\$ (modeling the service distance), and a bound~\$B\$ on the total service distance. The goal is to find a subtree~\$T\$ of \$G\$ with minimum \$c\$-cost \$c(T)\$ subject to the constraint that the sum of the service distances of all the remaining nodes \$v \in V\setminus T\$ to their closest neighbor in~\$T\$ does not exceed the specified budget~\$B\$. This problem has applications in optical network design and the efficient maintenance of distributed databases. We formulate this problem as bicriteria network design problem, and present bicriteria approximation algorithms. We also prove lower bounds on the approximability of the problem that demonstrate that our performance ratios are close to best possible}, language = {en} } @misc{GroetschelKrumkeRambau1999, author = {Gr{\"o}tschel, Martin and Krumke, Sven and Rambau, J{\"o}rg}, title = {Wo bleibt der Aufzug?}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4175}, number = {SC-99-29}, year = {1999}, abstract = {Dieser Artikel gibt eine allgemeinverst{\"a}ndliche Einf{\"u}hrung in die spezielle Problematik kombinatorischer Online-Problem am Beispiel der Fahrstuhlsteuerung.}, language = {de} } @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} }