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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of combinatorial optimization 2 (1998), S. 257-288 
    ISSN: 1573-2886
    Keywords: Complexity ; NP-hardness ; Approximation Algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study budget constrained network upgrading problems. Such problems aim at finding optimal strategies for improving a network under some cost measure subject to certain budget constraints. Given an edge weighted graph G = (V, E), in the edge based upgrading model, it is assumed that each edge e of the given network also has an associated function ce (t) that specifies the cost of upgrading the edge by an amount t. A reduction strategy specifies for each edge e the amount by which the length ℓ(e) is to be reduced. In the node based upgrading model, a node v can be upgraded at an expense of c(v). Such an upgrade reduces the delay of each edge incident on v. For a given budget B, the goal is to find an improvement strategy such that the total cost of reduction is at most the given budget B and the cost of a subgraph (e.g. minimum spanning tree) under the modified edge lengths is the best over all possible strategies which obey the budget constraint. After providing a brief overview of the models and definitions of the various problems considered, we present several new results on the complexity and approximability of network improvement problems.
    Type of Medium: Electronic Resource
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  • 2
    Book
    Book
    Berlin :Konrad-Zuse-Zentrum,
    Title: Online optimization : competitive analysis and beyond; 02-25
    Author: Krumke, Sven O.
    Publisher: Berlin :Konrad-Zuse-Zentrum,
    Year of publication: 2002
    Pages: 176 S.
    Series Statement: ZIB-Report 02-25
    Type of Medium: Book
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  • 3
    Title: Graphentheoretische Konzepte und Algorithmen /
    Author: Krumke, Sven Oliver
    Contributer: Noltemeier, Hartmut
    Edition: 1. Aufl.
    Publisher: Wiesbaden :Teubner,
    Year of publication: 2005
    Pages: X, 407 S. : , graph. Darst.
    Series Statement: Leitfäden der angewandten Informatik
    ISBN: 3-519-00526-3
    Type of Medium: Book
    Language: German
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  • 4
    Title: Online optimization of large scale systems
    Contributer: Grötschel, Martin , Krumke, Sven O. , Rambau, Jörg
    Publisher: Berlin u.a. :Springer,
    Year of publication: 2001
    Pages: 801 S.
    Type of Medium: Book
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  • 5
    Publication Date: 2020-11-13
    Description: Dieser Artikel gibt eine allgemeinverständliche Einführung in die spezielle Problematik kombinatorischer Online-Problem am Beispiel der Fahrstuhlsteuerung.
    Keywords: ddc:000
    Language: German
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 6
    Publication Date: 2020-11-13
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 7
    Publication Date: 2020-11-13
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 8
    Publication Date: 2020-11-13
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 9
    Publication Date: 2020-11-13
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 10
    Publication Date: 2020-11-13
    Description: 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.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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