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  • 1
    Electronic Resource
    Electronic Resource
    A polyhedral approach to multicommodity survivable network design (1994)
    Springer
    Numerische Mathematik 68 (1994), S. 149-167 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 65K05, 90C35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. The design of cost-efficient networks satisfying certain survivability constraints is of major concern to the telecommunications industry. In this paper we study a problem of extending the capacity of a network by discrete steps as cheaply as possible, such that the given traffic demand can be accommodated even when a single edge or node in the network fails. We derive valid and nonredundant inequalities for the polyhedron of capacity design variables, by exploiting its relationship to connectivity network design and knapsack-like subproblems. A cutting plane algorithm and heuristics for the problem are described, and preliminary computational results are reported.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050054
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Weakk-majorization and polyhedra (1998)
    Springer
    Mathematical programming 81 (1998), S. 37-53 
    Details
    ISSN: 1436-4646
    Keywords: Majorization ; Polyhedra
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract For integersk andn withk ⩽ n a vectorx ∈ ℝ n is said to be weaklyk-majorized by a vectorq ∈ ℝ k if the sum of ther largest components ofx does not exceed the sum of ther largest components ofq, forr = 1,⋯,k. For a givenq the set of vectors weaklyk-majorized byq defines a polyhedronP(q; k). We determine the vertices of bothP(q; k) and its integer hullQ(q; k). Furthermore a complete and nonredundant linear description ofQ(q; k) is given. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584843
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    The design of survivable directed networks (1993)
    Springer
    Telecommunication systems 2 (1993), S. 349-377 
    Details
    ISSN: 1572-9451
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We study a survivable network design problem:the directed network design problem with connectivity constraints (DNCC). Some applications in telecommunications are presented. We discuss two integer linear programming models for DNCC, and relate these. The main body of the paper is a study of DNCC from a polyhedral point of view. We give several classes of nonredundant inequalities for polytopes associated with the problem. A cutting plane algorithm based on the polyhedral results is described and some computational results are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02109865
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    Paper (German National Licenses)
    Fulltext
  • 4
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    A Polyhedral Approach to Multicommodity Survivable Network Design. (1993)
    Details
    Publication Date: 2014-02-26
    Description: The design of cost-efficient networks satisfying certain survivability constraints is of major concern to the telecommunications industry. In this paper we study a problem of extending the capacity of a network by discrete steps as cheaply as possible, such that the given traffic demand can be accommodated even when a single edge or node in the network fails. We derive valid and non-redundant inequalities for the polyhedron of capacity design variables, by exploiting its relationship to connectivity network design and knapsack-like subproblems. Computational work using this model and the additional inequalities is in progress.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
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    OPUS
  • 5
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    Routing through virtual paths in layered telecommunication networks (1995)
    Details
    Publication Date: 2014-02-26
    Description: We study a network configuration problem in telecommunications where one wants to set up paths in a capacitated network to accommodate given point-to-point traffic demand. The problem is formulated as an integer linear programming model where 0-1 variables represent different paths. An associated integral polytope is studied and different classes of facets are described. These results are used in a cutting plane algorithm. Computational results for some realistic problems are reported.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
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    OPUS
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