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  • 1
    Electronic Resource
    Electronic Resource
    Cost-efficient network synthesis from leased lines (1998)
    Springer
    Annals of operations research 76 (1998), S. 1-20 
    Details
    ISSN: 1572-9338
    Keywords: telecommunication network design, survivable networks, network capacity planning, cutting plane algorithm, heuristics, routing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Given a communication demand between each pair of nodes of a network, we consider the problem of deciding what capacity to install on each edge of the network in order to minimize the building cost of the network and to satisfy a given demand between each pair of nodes. The feasible capacities that can be leased from a network provider are of a particular kind in our case. There are a few so-called basic capacities having the property that every basic capacity is an integral multiple of every smaller basic capacity. An edge can be equipped with a capacity only if it is an integer combination of the basic capacities. In addition, we treat several restrictions on the routings of the demands (length restriction, diversification) and failures of single nodes or single edges. We formulate the problem as a mixed integer linear programming problem and develop a cutting plane algorithm as well as several heuristics to solve it. We report on computational results for real-world data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018984102311
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    The convex hull of a linear congruence relation in zero-one variables (1995)
    Springer
    Mathematical methods of operations research 41 (1995), S. 1-23 
    Details
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A class of optimization problems over subsets of zero-one vectors of then-dimensional unit cube given by a special linear congruence relation is considered. The general problem is formulated as a zero-one linear program, minimal and complete descriptions of the associated polytopes by linear inequalities are derived and an $$\mathcal{O}(n \log n)$$ time algorithm for the optimization problems is given. Since the number of inequalities that completely describe the polytope grows exponentially withn, we also give a separation algorithm that identifies violated inequalities in time $$\mathcal{O}(n^2 )$$ . A particular variation of the bin packing problem is a special case of our problem and can thus be solved in polynomial time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01415061
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    Paper (German National Licenses)
    Fulltext
  • 3
    Book
    Book
    Linear optimization and extensions : problems and solutions (2001)
    Berlin u.a. :Springer,
    Details
    Title: Linear optimization and extensions : problems and solutions
    Author: Alevras, Dimitris
    Contributer: Padberg, Manfred W.
    Publisher: Berlin u.a. :Springer,
    Year of publication: 2001
    Pages: 449 S.
    Series Statement: Universitext
    Type of Medium: Book
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    ZIB Catalog
    Zuse Institute Berlin get availability status
  • 4
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    Cost-Efficient Network Synthesis from Leased Lines (1997)
    Details
    Publication Date: 2014-02-26
    Description: Given a communication demand between each pair of nodes of a network we consider the problem of deciding what capacity to install on each edge of the network in order to minimize the building cost of the network and to satisfy the demand between each pair of nodes. The feasible capacities that can be leased from a network provider are of a particular kind in our case. There are a few so-called basic capacities having the property that every basic capacity is an integral multiple of every smaller basic capacity. An edge can be equipped with a capacity only if it is an integer combination of the basic capacities. We treat, in addition, several restrictions on the routings of the demands (length restriction, diversification) and failures of single nodes or single edges. We formulate the problem as a mixed integer linear programming problem and develop a cutting plane algorithm as well as several heuristics to solve it. We report on computational results for real world data.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 5
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    Capacity and Survivability Models for Telecommunication Networks (1997)
    Details
    Publication Date: 2020-08-05
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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    OPUS
  • 6
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    Survivable Mobile Phone Network Architectures (1998)
    Details
    Publication Date: 2020-08-05
    Language: English
    Type: article , doc-type:article
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    OPUS
  • 7
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    Cost-efficient network synthesis from leased lines (1998)
    Details
    Publication Date: 2020-08-05
    Language: English
    Type: article , doc-type:article
    Library Location Call Number Volume/Issue/Year Availability
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    OPUS
  • 8
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    Survivable Mobile Phone Architectures: Models and Solution Methods (1996)
    Details
    Publication Date: 2014-02-26
    Description: In the highly competitive area of telecommunications, cost, quality, and network management are among the most important aspects to be considered when designing a network. We study the problem of dimensioning a telecommunication network that is still operating in case of a failure of a network component. Given a demand between each pair of nodes of a telecommunication network and a finite set of possible capacities for each edge of the network, we consider the problem of deciding what capacity to install on each edge of the network in order to minimize the building cost of the network and to satisfy the demand between each pair of nodes, even if a network component fails. The routing of the demands must satisfy the following additional restrictions: (a) there is a maximum number of nodes allowed in each path between any pair of nodes (path length restriction), and (b) there is a maximum percentage of the demand between each pair of nodes that can be routed through any network component (diversification restriction). Moreover, the chosen capacities must be such that, for every single node or single edge failure, a certain percentage of the demand between any pair of nodes is reroutable (i.e. it ``survives'' the particular failure). We formulate the problem as a mixed integer linear programming problem and present a cutting plane algorithm as well as several heuristics for its solution. Furthermore, we discuss several ways to implement survivability into a telecommunication network.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 9
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    A Network Dimensioning Tool (1996)
    Details
    Publication Date: 2014-02-26
    Description: Designing low cost networks that survive certain failure situations belongs to one of the prime tasks in the telecommunications industry. In this paper we describe a mathematical model combining several aspects of survivability that are elsewhere treated in a hierarchical fashion. We present mathematical investigations of this integrated model, a cutting plane algorithm, as well as several heuristics for its solution. Moreover, we report computational results with real world data. The problem we address is the following. Suppose, between each pair of nodes in a region, a communication demand is given. We want to determine the topology of a telecommunication network connecting the given nodes and to dimension all potential physical links. For each link, the possible capacities are restricted to a given finite set. The capacities must be chosen such that the communication demands are satisfied, even if certain network components fail, and such that the network building costs are as small as possible. Moreover, for each pair of nodes and each failure situation, we want to determine the paths on which the demand between the nodes is routed.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 10
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    Capacity and Survivability Models for Telecommunication Networks (1997)
    Details
    Publication Date: 2014-02-26
    Description: Designing low-cost networks that survive certain failure situations is one of the prime tasks in the telecommunication industry. In this paper we survey the development of models for network survivability used in practice in the last ten years. We show how algorithms integrating polyhedral combinatorics, linear programming, and various heuristic ideas can help solve real-world network dimensioning instances to optimality or within reasonable quality guarantees in acceptable running times. The most general problem type we address is the following. Let a communication demand between each pair of nodes of a telecommunication network be given. We consider the problem of choosing, among a discrete set of possible capacities, which capacity to install on each of the possible edges of the network in order to (i) satisfy all demands, (ii) minimize the building cost of the network. \noindent In addition to determining the network topology and the edge capacities we have to provide, for each demand, a routing such that (iii) no path can carry more than a given percentage of the demand, (iv) no path in the routing exceeds a given length. \noindent We also have to make sure that (v) for every single node or edge failure, a certain percentage of the demand is reroutable. \noindent Moreover, for all failure situations feasible routings must be computed. The model described above has been developed in cooperation with a German mobile phone provider. We present a mixed-integer programming formulation of this model and computational results with data from practice.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
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