TY - GEN A1 - Heinz, Stefan A1 - Krumke, Sven A1 - Megow, Nicole A1 - Rambau, Jörg A1 - Tuchscherer, Andreas A1 - Vredeveld, Tjark T1 - The Online Target Date Assignment Problem N2 - Many online problems encountered in real-life involve a two-stage decision process: upon arrival of a new request, an irrevocable first-stage decision (the assignment of a specific resource to the request) must be made immediately, while in a second stage process, certain ``subinstances'' (that is, the instances of all requests assigned to a particular resource) can be solved to optimality (offline) later. We introduce the novel concept of an \emph{Online Target Date Assignment Problem} (\textsc{OnlineTDAP}) as a general framework for online problems with this nature. Requests for the \textsc{OnlineTDAP} become known at certain dates. An online algorithm has to assign a target date to each request, specifying on which date the request should be processed (e.\,g., an appointment with a customer for a washing machine repair). The cost at a target date is given by the \emph{downstream cost}, the optimal cost of processing all requests at that date w.\,r.\,t.\ some fixed downstream offline optimization problem (e.\,g., the cost of an optimal dispatch for service technicians). We provide general competitive algorithms for the \textsc{OnlineTDAP} independently of the particular downstream problem, when the overall objective is to minimize either the sum or the maximum of all downstream costs. As the first basic examples, we analyze the competitive ratios of our algorithms for the par ticular academic downstream problems of bin-packing, nonpreemptive scheduling on identical parallel machines, and routing a traveling salesman. T3 - ZIB-Report - 05-61 KW - Online Algorithms KW - Online Target Date Assignment Problem Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8945 ER - TY - CHAP A1 - Hiller, Benjamin A1 - Krumke, Sven A1 - Rambau, Jörg ED - Liebling, T. ED - Duran, G. ED - Matamala, M. T1 - Reoptimization Gaps versus Model Errors in Online-Dispatching of Service Units for ADAC T2 - Latin-American Conference on Combinatorics, Graphs and Applications, Santiago de Chile 2004 Y1 - 2004 VL - 18 SP - 157 EP - 163 ER - TY - JOUR A1 - Hiller, Benjamin A1 - Krumke, Sven A1 - Rambau, Jörg T1 - Reoptimization Gaps versus Model Errors in Online-Dispatching of Service Units for ADAC JF - DISAM Y1 - 2006 VL - 154 IS - 13 SP - 1897 EP - 1907 ER - TY - GEN A1 - Ascheuer, Norbert A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg T1 - Combinatorial Online Optimization N2 - In ``classical'' optimization, all data of a problem instance are considered given. The standard theory and the usual algorithmic techniques apply to such cases only. Online optimization is different. Many decisions have to be made before all data are available. In addition, decisions once made cannot be changed. How should one act ``best'' in such an environment? In this paper we survey online problems coming up in combinatorial optimization. We first outline theoretical concepts, such as competitiveness against various adversaries, to analyze online problems and algorithms. The focus, however, lies on real-world applications. We report, in particular, on theoretical investigations and our practical experience with problems arising in transportation and the automatic handling of material. T3 - ZIB-Report - SC-98-24 KW - Online Optimization KW - competitiveness KW - combinatorial optimization KW - real-world problems Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3674 ER - TY - GEN A1 - Ascheuer, Norbert A1 - Krumke, Sven A1 - Rambau, Jörg T1 - The Online Transportation Problem: Competitive Scheduling of Elevators N2 - In this paper we consider the following online transportation problem (\textsc{Oltp}): Objects are to be transported between the vertices of a given graph. Transportation requests arrive online, specifying the objects to be transported and the corresponding source and target vertex. These requests are to be handled by a server which commences its work at a designated origin vertex and which picks up and drops objects at their starts and destinations. After the end of its service the server returns to its start. The goal of \textsc{Oltp} is to come up with a transportation schedule for the server which finishes as early as possible. We first show a lower bound of~$5/3$ for the competitive ratio of any deterministic algorithm. We then analyze two simple and natural strategies which we call \textsf{REPLAN} and \textsf{IGNORE}. \textsf{REPLAN} completely discards its schedule and recomputes a new one when a new request arrives. \textsf{IGNORE} always runs a (locally optimal) schedule for a set of known requests and ignores all new requests until this schedule is completed. We show that both strategies, \textsf{REPLAN} and \textsf{IGNORE}, are $5/2$-competitive. We also present a somewhat less natural strategy \textsf{SLEEP}, which in contrast to the other two strategies may leave the server idle from time to time although unserved requests are known. We also establish a competitive ratio of~$5/2$ for the algorithm \textsf{SLEEP}. Our results are extended to the case of ``open schedules'' where the server is not required to return to its start position at the end of its service. T3 - ZIB-Report - SC-98-34 KW - online optimization KW - competitive analysis KW - elevator Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3779 ER - TY - CHAP A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg A1 - Winter, Thomas A1 - Zimmermann, Uwe ED - Grötschel, Martin ED - Krumke, Sven ED - Rambau, Jörg T1 - Combinatorial Online Optimization in Real Time T2 - Online Optimization of Large Scale Systems Y1 - 2001 SP - 679 EP - 704 PB - Springer ER - TY - CHAP A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg ED - Grötschel, Martin ED - Krumke, Sven ED - Rambau, Jörg T1 - Online Optimization of Complex Transportation Systems T2 - Online Optimization of Large Scale Systems Y1 - 2001 SP - 705 EP - 729 PB - Springer 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 - Krumke, Sven A1 - Rambau, Jörg A1 - Torres, Luis Miguel T1 - Online-Dispatching of Automobile Service Units N2 - We present an online algorithm for a real-world vehicle dispatching problem at ADAC, the German Automobile Association. T3 - ZIB-Report - 02-44 KW - vehicle dispatching KW - soft time windows KW - online KW - real-time KW - ADAC Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7117 ER - TY - GEN A1 - Hülsermann, Ralf A1 - Jäger, Monika A1 - Krumke, Sven A1 - Poensgen, Diana A1 - Rambau, Jörg A1 - Tuchscherer, Andreas T1 - Dynamic Routing Algorithms in Transparent Optical Networks An Experimental Study Based on Real Data N2 - Today's telecommunication networks are configured statically. Whenever a connection is established, the customer has permanent access to it. However, it is observed that usually the connection is not used continuously. At this point, dynamic provisioning could increase the utilization of network resources. WDM based Optical Transport Networks (OTNs) will shortly allow for fast dynamic network reconfiguration. This enables optical broadband leased line services on demand. Since service requests competing for network resources may lead to service blocking, it is vital to use appropriate strategies for routing and wavelength assignment in transparent optical networks. We simulate the service blocking probabilities of various dynamic algorithms for this problem using a well-founded traffic model for two realistic networks. One of the algorithms using shortest path routings performs best on all instances. Surprisingly, the tie-breaking rule between equally short paths in different wavelengths decides between success or failure. T3 - ZIB-Report - 02-35 KW - Dynamic Network Configuration KW - Routing and Wavelength Allocation KW - Transparent Optical Networks KW - Blocking Probability KW - Simulation Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7025 ER - TY - GEN A1 - Krumke, Sven A1 - Laura, Luigi A1 - Lipmann, Maarten A1 - Marchetti-Spaccamela, Alberto A1 - Paepe, Willem de A1 - Poensgen, Diana A1 - Stougie, Leen T1 - Non-Abusiveness Helps: An O(1)-Competitive Algorithm for Minimizing the Maximum Flow Time in the Online Traveling Salesman Problem N2 - 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. T3 - ZIB-Report - 02-36 KW - Online Algorithms KW - Competitive Analysis KW - Comparative Analysis Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7038 ER - TY - GEN A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg A1 - Torres, Luis Miguel T1 - Making the Yellow Angels Fly: Online Dispatching Of Service Vehicles in Real Time N2 - 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. T3 - ZIB-Report - 02-18 KW - vehicle dispatching KW - soft time windows KW - real-time KW - column generation KW - pricing KW - branch and bound KW - real world data KW - ADAC Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6858 ER - TY - GEN A1 - Krumke, Sven A1 - Poensgen, Diana T1 - Online Call Admission in Optical Networks with Larger Wavelength Demands N2 - 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. T3 - ZIB-Report - 02-22 KW - Call Admission KW - Routing and Wavelength Allocation KW - Optical Networks KW - Competitive Analysis KW - Colorability Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6890 ER - TY - GEN A1 - Krumke, Sven A1 - Lipmann, Maarten A1 - Paepe, Willem de A1 - Poensgen, Diana A1 - Rambau, Jörg A1 - Stougie, Leen A1 - Woeginger, Gerhard T1 - How to Cut a Cake Almost Fairly N2 - 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. T3 - ZIB-Report - 02-23 KW - Fair division KW - cake cutting Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6905 ER - TY - GEN A1 - Krumke, Sven A1 - Marathe, Madhav A1 - Poensgen, Diana A1 - Ravi, Sekharipuram S. A1 - Wirth, Hans-Christoph T1 - Budgeted Maximal Graph Coverage N2 - 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. T3 - ZIB-Report - 02-24 KW - budgeted maximum coverage KW - approximation algorithm KW - dynamic programming Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6918 ER - TY - GEN A1 - Krumke, Sven T1 - News from the Online Traveling Repairman N2 - 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. T3 - ZIB-Report - 00-08 KW - Traveling Repairman KW - Latency KW - Dial-a-Ride-Problem KW - Competitive Analysis Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5767 ER - TY - GEN A1 - Blom, Michiel A1 - Krumke, Sven A1 - Paepe, Willem de A1 - Stougie, Leen T1 - The Online-TSP Against Fair Adversaries N2 - 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. T3 - ZIB-Report - 00-09 KW - Vehicle Routing KW - Online-Algorithms KW - Competitive Analysis Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5779 ER - TY - GEN A1 - Konjevod, Goran A1 - Krumke, Sven A1 - Marathe, Madhav T1 - Budget Constrained Minimum Cost Connected Medians N2 - 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 T3 - ZIB-Report - 00-10 KW - NP-hardness KW - Approximation Algorithms KW - Network Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5783 ER - TY - GEN A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg T1 - Wo bleibt der Aufzug? N2 - Dieser Artikel gibt eine allgemeinverständliche Einführung in die spezielle Problematik kombinatorischer Online-Problem am Beispiel der Fahrstuhlsteuerung. T3 - ZIB-Report - SC-99-29 KW - Aufzugsteuerung KW - Online-Optimierung KW - Echtzeit-Optimierung KW - kompetitive Analyse Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4175 ER - TY - GEN A1 - Hauptmeier, Dietrich A1 - Krumke, Sven A1 - Rambau, Jörg A1 - Wirth., Hans-Christoph T1 - Euler is Standing in Line N2 - 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~$5/3$. T3 - ZIB-Report - SC-99-06 KW - NP-completeness KW - polynomial-time approximation algorithms KW - stacker-crane problem KW - vehicle routing KW - elevator system KW - Eulerian Cycle Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3947 ER - TY - GEN A1 - Hauptmeier, Dietrich A1 - Krumke, Sven A1 - Rambau, Jörg T1 - The Online Dial-a-Ride Problem under Reasonable Load N2 - In this paper, we analyze algorithms for the online dial-a-ride problem with request sets that fulfill a certain worst-case restriction: roughly speaking, a set of requests for the online dial-a-ride problem is reasonable if the requests that come up in a sufficiently large time period can be served in a time period of at most the same length. This new notion is a stability criterion implying that the system is not overloaded. The new concept is used to analyze the online dial-a-ride problem for the minimization of the maximal resp.\ average flow time. Under reasonable load it is possible to distinguish the performance of two particular algorithms for this problem, which seems to be impossible by means of classical competitive analysis. T3 - ZIB-Report - SC-99-08 KW - online optimization KW - competitive analysis KW - elevator Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3961 ER - TY - GEN A1 - Grötschel, Martin A1 - Hauptmeier, Dietrich A1 - Krumke, Sven A1 - Rambau, Jörg T1 - Simulation Studies for the Online-Dial-a-Ride Problem N2 - In a large distribution center of Herlitz AG, Berlin, we invesigated the elevator subsystem of the fully automated pallet transportation system. Each elevator may carry one pallet and has to serve eight levels. The goal is to minimize the average resp.\ the maximum flow time. The variants of this elevator control problem have been subject of recent theoretical research and are known as online-dial-a-ride problems. In this paper we investigate several online algorithms for several versions of online-dial-a-ride problems by means of a simulation program, developed on the basis of the simulation library AMSEL. We draw statistics from samples of randomly generated data providing for different load situations. Moreover, we provide preliminary studies with real production data for a system of five elevators connected by a conveyor circuit, as can be found at the Herlitz plant. We show which algorithms are best under certain load situations and which lead to break downs under particular circumstances. T3 - ZIB-Report - SC-99-09 KW - online optimization KW - competitive analysis KW - elevator KW - simulation studies Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-3976 ER - TY - GEN A1 - Hiller, Benjamin A1 - Krumke, Sven A1 - Rambau, Jörg T1 - Reoptimization Gaps versus Model Errors in Online-Dispatching of Service Units for ADAC N2 - Under high load, the automated dispatching of service vehicles for the German Automobile Association (ADAC) must reoptimize a dispatch for 100--150 vehicles and 400 requests in about ten seconds to near optimality. In the presence of service contractors, this can be achieved by the column generation algorithm ZIBDIP. In metropolitan areas, however, service contractors cannot be dispatched automatically because they may decline. The problem: a model without contractors yields larger optimality gaps within ten seconds. One way-out are simplified reoptimization models. These compute a short-term dispatch containing only some of the requests: unknown future requests will influence future service anyway. The simpler the models the better the gaps, but also the larger the model error. What is more significant: reoptimization gap or reoptimization model error? We answer this question in simulations on real-world ADAC data: only the new model ZIBDIP{\footnotesize dummy} can keep up with ZIBDIP. T3 - ZIB-Report - 04-17 KW - vehicle dispatching KW - soft time windows KW - online KW - real-time KW - ADAC KW - optimality gap KW - high load Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7928 ER - TY - GEN A1 - Krumke, Sven A1 - Noltemeier, Hartmut A1 - Wirth, Hans-Christoph T1 - Graphentheoretische Konzepte und Algorithmen N2 - Das vorliegende Skript bietet eine Einf{ü}hrung in die Graphentheorie und graphentheoretische Algorithmen. Im zweiten Kapitel werden Grundbegriffe der Graphentheorie vorgestellt. Das dritte Kapitel besch{ä}ftigt sich mit der Existenz von Wegen in Graphen. Hier wird auch die L{ö}suung des ber{ü}hmten K{ö}nigsberger Br{ü}ckenproblems aufgezeigt und der Satz von Euler bewiesen. Im vierten Kapitel wird gezeigt, wie man auf einfache Weise die Zusammenhangskomponenten eines Graphen bestimmen kann. Im Kapitel sechs wird dann sp{ä}ter mit der Tiefensuche ein Verfahren vorgestellt, das schneller arbeitet und mit dessen Hilfe man noch mehr Informationen {ü}ber die Struktur eines Graphen gewinnen kann. In den folgenden Kapiteln werden Algorithmen vorgestellt, um minimale aufspannenden B{ä}ume, k{ü}rzeste Wege und maximale Fl{ü}sse in Graphen zu bestimmen. Am Ende des Skripts wird ein kurzer Einblick in die planaren Graphen und Graphhomomorphismen geboten. T3 - ZIB-Report - 00-19 KW - Graphen KW - Algorithmen KW - Komplexit{ä}t KW - kombinatorische Optimierung Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5873 ER - TY - GEN A1 - Krumke, Sven A1 - Rambau, Jörg A1 - Weider, Steffen T1 - An Approximation Algorithm for the Non-Preemptive Capacitated Dial-a-Ride Problem N2 - In the Capacitated Dial-a-Ride Problem (CDARP) we are given a transportation network and a finite set of transportation jobs. Each job specifies the source and target location which are both part of the network. A server which can carry at most $C$~objects at a time can move on the transportation network in order to process the transportation requests. The problem CDARP consists of finding a shortest transportation for the jobs starting and ending at a designated start location. In this paper we are concerned with the restriction of CDARP to graphs which are simple paths. This setting arises for instance when modelling applications in elevator transportation systems. It is known that even for this restricted class of graphs CDARP is NP-hard to solve. We provide a polynomial time approximation algorithm that finds a transportion of length at most thrice the length of the optimal transportation. T3 - ZIB-Report - 00-53 KW - NP-completeness KW - polynomial-time approximation algorithms KW - stacker-crane problem KW - vehicle Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6217 ER - TY - GEN A1 - Krumke, Sven A1 - Rambau, Jörg T1 - Online Optimierung N2 - Wie soll man einen Aufzug steuern, wenn man keine Informationen über zukünftige Fahraufträge besitzt? Soll man eine Bahncard kaufen, wenn die nächsten Bahnreisen noch unbekannt sind? In der klassischen kombinatorischen Optimierung geht man davon aus, daß die Daten jeder Probleminstanz vollständig gegeben sind. In vielen Fällen modelliert diese \emph{Offline-Optimierung} jedoch die Situationen aus Anwendungen nur ungenügend. Zahlreiche Problemstellungen in der Praxis sind in natürlicher Weise \emph{online}: Sie erfordern Entscheidungen, die unmittelbar und ohne Wissen zukünftiger Ereignisse getroffen werden müssen. Als ein Standardmittel zur Beurteilung von Online-Algorithmen hat sich die \emph{kompetitive Analyse} durchgesetzt. Dabei vergleicht man den Zielfunktionswert einer vom Online-Algorithmus generierten Lösung mit dem Wert einer optimalen Offline-Lösung. Mit Hilfe der kompetitiven Analyse werden im Skript Algorithmen zum Caching, Netzwerk-Routing, Scheduling und zu Transportaufgaben untersucht. Auch die Schwächen der kompetitiven Analyse werden aufgezeigt und alternative Analysekonzepte vorgestellt. Neben der theoretischen Seite werden auch die Anwendungen der Online-Optimierung in der Praxis, vor allem bei Problemen der innerbetrieblichen Logistik, beleuchtet. Bei der Steuerung automatischer Transportsysteme tritt eine Fülle von Online-Problemen auf. Hierbei werden an die Algorithmen oftmals weitere Anforderungen gestellt. So müssen Entscheidungen unter strikten Zeitbeschränkungen gefällt werden (Echtzeit-Anforderungen). Dieses Skript ist aus dem Online-Teil der Vorlesung -Ausgewählte Kapitel aus der ganzzahligen Optimierung- (Wintersemester~1999/2000) und der Vorlesung -Online Optimierung- (Sommersemester~2000) an der Technischen Universität Berlin entstanden. T3 - ZIB-Report - 00-55 KW - Kompetitive Analyse KW - Online Optimierung KW - Online Algorithmen Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6238 ER - TY - GEN A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg A1 - Winter, Thomas A1 - Zimmermann, Uwe T1 - Combinatorial Online Optimization in Real Time N2 - Optimization is the task of finding an optimum solution to a given problem. When the decision variables are discrete we speak of a combinatorial optimization problem. Such a problem is online when decisions have to be made before all data of the problem are known. And we speak of a real-time online problem when online decisions have to be computed within very tight time bounds. This paper surveys the are of combinatorial online and real-time optimization, it discusses, in particular, the concepts with which online and real-time algorithms can be analyzed. T3 - ZIB-Report - 01-16 KW - Online Optimization KW - Realtime Optimization KW - Competitive Analysis KW - Heuristics KW - Survey Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6424 ER - TY - GEN A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg T1 - Online Optimization of Complex Transportation Systems N2 - This paper discusses online optimization of real-world transportation systems. We concentrate on transportation problems arising in production and manufacturing processes, in particular in company internal logistics. We describe basic techniques to design online optimization algorithms for such systems, but our main focus is decision support for the planner: which online algorithm is the most appropriate one in a particular setting? We show by means of several examples that traditional methods for the evaluation of online algorithms often do not suffice to judge the strengths and weaknesses of online algorithms. We present modifications of well-known evaluation techniques and some new methods, and we argue that the selection of an online algorithm to be employed in practice should be based on a sound combination of several theoretical and practical evaluation criteria, including simulation. T3 - ZIB-Report - 01-17 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6438 ER - TY - GEN A1 - Krumke, Sven A1 - Rambau, Jörg A1 - Torres, Luis Miguel T1 - Real-Time Dispatching of Guided and Unguided Automobile Service Units with Soft Time Windows N2 - Given a set of service requests (events), a set of guided servers (units), and a set of unguided service contractors (conts), the vehicle dispatching problem {\sl vdp} is the task to find an assignment of events to units and conts as well as tours for all units starting at their current positions and ending at their home positions (dispatch) such that the total cost of the dispatch is minimized. The cost of a dispatch is the sum of unit costs, cont costs, and event costs. Unit costs consist of driving costs, service costs and overtime costs; cont costs consist of a fixed cost per service; event costs consist of late costs linear in the late time, which occur whenever the service of the event starts later than its deadline. The program \textsf{ZIBDIP} based on dynamic column generation and set partitioning yields solutions on heavy-load real-world instances (215 events, 95 units) in less than a minute that are no worse than 1\% from optimum on state-of-the-art personal computers. T3 - ZIB-Report - 01-22 KW - vehicle dispatching KW - soft time windows KW - real-time KW - column generation KW - pricing KW - branch and bound KW - real world data KW - ADAC Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6484 ER - TY - GEN A1 - Krumke, Sven A1 - Paepe, Willem de A1 - Rambau, Jörg A1 - Stougie, Leen T1 - Online Bin-Coloring N2 - 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. T3 - ZIB-Report - 01-07 KW - Online Optimization KW - randomized algorithms KW - lower bounds KW - competitive analysis Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6338 ER - TY - GEN A1 - Krumke, Sven A1 - Rambau, Jörg T1 - Probieren geht über Studieren? Entscheidungshilfen für kombinatorische Online-Optimierungsprobleme in der innerbetrieblichen Logistik N2 - Die Automatisierung von innerbetrieblicher Logistik erfordert -- über die physikalische Steuerung von Geräten hinaus -- auch eine effiziente Organisation der Transporte: ein Aufgabenfeld der kombinatorischen Optimierung. Dieser Artikel illustriert anhand von konkreten Aufgabenstellungen die Online-Problematik (unvollständiges Wissen) sowie die Echtzeit-Problematik (beschränkte Rechenzeit), auf die man in der innerbetrieblichen Logistik trifft. Der Text gibt einen Überblick über allgemeine Konstruktionsprinzipien für Online-Algorithmen und Bewertungsmethoden, die bei der Entscheidung helfen, welche Algorithmen für eine vorliegende Problemstellung geeignet sind. T3 - ZIB-Report - 02-05 KW - Logistik KW - Hochregallagerbediengeräte KW - Kommissioniermobile KW - Aufzüge KW - Online-Optimierung KW - Echtzeit-Optimierung KW - Simulation KW - kompetitive Analyse Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6723 ER - TY - JOUR A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg A1 - Torres, Luis Miguel T1 - Making the Yellow Angels Fly JF - SIAM News Y1 - 2002 VL - 35 IS - 4 SP - 1,10,11 ER - TY - JOUR A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg T1 - Wo bleibt der Aufzug? JF - OR News Y1 - 1999 VL - 5 SP - 11 EP - 13 ER - TY - JOUR A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg T1 - Wo bleibt der Aufzug? JF - OR News Y1 - 2006 VL - Sonderausgabe SP - 70 EP - 72 ER - TY - CHAP A1 - Ascheuer, Norbert A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg ED - Kall, Peter ED - Lüthi, Hans-Jakob T1 - Combinatorial Online Optimization T2 - Operations Research Proceedings 1998. Selected Papers of the International Conference on Operations Research Zurich, August 31 – September 3, 1998 Y1 - 1999 SP - 21 EP - 37 PB - Springer ER - TY - CHAP A1 - Heinz, Stefan A1 - Krumke, Sven A1 - Megow, Nicole A1 - Rambau, Jörg A1 - Tuchscherer, Andreas A1 - Vredeveld, Tjark ED - Erlebach, Thomas ED - Persiano, Giuseppe T1 - The Online Target Date Assignment Problem T2 - Proc. 3rd Workshop on Approximation and Online Algorithms Y1 - 2006 UR - http://opus.kobv.de/zib/volltexte/2005/894/ VL - 3879 SP - 230 EP - 243 PB - Springer ER - TY - CHAP A1 - Hiller, Benjamin A1 - Krumke, Sven A1 - Saliba, Sleman A1 - Tuchscherer, Andreas T1 - Randomized Online Algorithms for Dynamic Multi-Period Routing Problems T2 - Proceedings of MAPSP Y1 - 2009 SP - 71 EP - 73 ER - TY - CHAP A1 - Hülsermann, Ralf A1 - Jäger, Monika A1 - Poensgen, Diana A1 - Krumke, Sven A1 - Rambau, Jörg A1 - Tuchscherer, Andreas ED - Cinkler, Tibor ED - Jakab, Tivadar ED - Tapolcai, Jànos ED - Gàspàr, Csaba T1 - Dynamic routing algorithms in transparent optical networks T2 - Proceedings of the 7th IFIP Working Conference on Optical Network Design & Modelling (ONDM 2003) Y1 - 2003 UR - http://opus.kobv.de/zib/volltexte/2002/703/ SP - 293 EP - 312 PB - Kluwer Academic Press ER - TY - GEN A1 - Hiller, Benjamin A1 - Krumke, Sven A1 - Saliba, Sleman A1 - Tuchscherer, Andreas T1 - Randomized Online Algorithms for Dynamic Multi-Period Routing Problems N2 - The Dynamic Multi-Period Routing Problem DMPRP introduced by Angelelli et al. gives a model for a two-stage online-offline routing problem. At the beginning of each time period a set of customers becomes known. The customers need to be served either in the current time period or in the following. Postponed customers have to be served in the next time period. The decision whether to postpone a customer has to be done online. At the end of each time period, an optimal tour for the customers assigned to this period has to be computed and this computation can be done offline. The objective of the problem is to minimize the distance traveled over all planning periods assuming optimal routes for the customers selected in each period. We provide the first randomized online algorithms for the DMPRP which beat the known lower bounds for deterministic algorithms. For the special case of two planning periods we provide lower bounds on the competitive ratio of any randomized online algorithm against the oblivious adversary. We identify a randomized algorithm that achieves the optimal competitive ratio of $\frac{1+\sqrt{2}}{2}$ for two time periods on the real line. For three time periods, we give a randomized algorithm that is strictly better than any deterministic algorithm. T3 - ZIB-Report - 09-03 KW - Online-Optimierung KW - Randomisierte Algorithmen KW - Zweistufiges Problem KW - Traveling-Salesman-Problem KW - online optimization KW - randomized algorithm KW - two-stage problem KW - traveling salesman problem Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11132 SN - 1438-0064 ER - TY - THES A1 - Krumke, Sven T1 - Online Optimization: Competitive Analysis and Beyond N2 - 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. T3 - ZIB-Report - 02-25 KW - competitive analysis KW - online optimization KW - online algorithm KW - approximation algorithm Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6925 ER -