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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 88 (2000), S. 425-450 
    ISSN: 1436-4646
    Keywords: Key words: set packing – polyhedral combinatorics – cutting planes – integer programming ; Mathematics Subject Classification (2000): 90C10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. This paper is about set packing relaxations of combinatorial optimization problems associated with acyclic digraphs and linear orderings, cuts and multicuts, and set packings themselves. Families of inequalities that are valid for such a relaxation as well as the associated separation routines carry over to the problems under investigation.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-5217
    Keywords: clustering problem ; design of main frame computers ; graph partitioning problem ; hypergraph partitioning problem ; integer programming ; mathematical modelling ; multiple knapsack problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper we describe and discuss a problem that arises in the (global) design of a main frame computer. The task is to assign certain functional units to a given number of so called multi chip modules or printed circuit boards taking into account many technical constraints and minimizing a complex objective function. We describe the real world problem. A thorough mathematical modelling of all aspects of this problem results in a rather complicated integer program that seems to be hopelessly difficult — at least for the present state of integer programming technology. We introduce several relaxations of the general model, which are alsoNP-hard, but seem to be more easily accessible. The mathematical relations between the relaxations and the exact formulation of the problem are discussed as well.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical methods of operations research 47 (1998), S. 1-37 
    ISSN: 1432-5217
    Keywords: Integer programming ; test set ; Graver test set ; Hilbert basis ; neighbors of the origin ; Gröbner basis ; augmentation problem ; knapsack problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This article is a survey about recent developments in the area of test sets of families of linear integer programs. Test sets are finite subsets of the integer lattice that allow to improve any given feasible non-optimal point of an integer program by one element in the set. There are various possible ways of defining test sets depending on the view that one takes: theGraver test set is naturally derived from a study of the integral vectors in cones; theScarf test set (neighbors of the origin) is strongly connected to the study of lattice point free convex bodies; the so-calledreduced Gröbner basis of an integer program is obtained from a study of generators of polynomial ideals. This explains why the study of test sets connects various branches of mathematics. We introduce in this paper these three kinds of test sets and discuss relations between them. We also illustrate on various examples such as the minimum cost flow problem, the knapsack problem and the matroid optimization problem how these test sets may be interpreted combinatorially. From the viewpoint of integer programming a major interest in test sets is their relation to the augmentation problem. This is discussed here in detail. In particular, we derive a complexity result of the augmentation problem, we discuss an algorithm for solving the augmentation problem by computing the Graver test set and show that, in the special case of an integer knapsack problem with 3 coefficients, the augmentation problem can be solved in polynomial time.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical methods of operations research 41 (1995), S. 255-275 
    ISSN: 1432-5217
    Keywords: Routing in VLSI-design ; Switchbox Routing ; Steiner Tree ; Steiner Tree Packing ; Cutting Plane Algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper we study the following problem, which we call the weighted routing problem. Let be given a graphG = (V, E) with non-negative edge weightsw e ∈ ℝ+ and letN,N ≥ 1, be a list of node sets. The weighted routing problem consists in finding mutually disjoint edge setsS 1,...,S N such that, for eachk ∈ {1, ...,N}, the subgraph (V(S k),S k) contains an [s, t]-path for alls, t ∈ T k and the sum of the weights of the edge sets is minimal. Our motivation for studying this problem arises from the routing problem in VLSI-design, where given sets of points have to be connected by wires. We consider the weighted routing problem from a polyhedral point of view. We define an appropriate polyhedron and try to (partially) describe this polyhedron by means of inequalities. We describe our separation algorithms for some of the presented classes of inequalities. Based on these separation routines we have implemented a branch and cut algorithm. Our algorithm is applicable to an important subclass of routing problems arising in VLSI-design, namely to switchbox routing problems where the underlying graph is a grid graph and the list of node sets is located on the outer face of the grid. We report on our computational experience with this class of problem instances.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical methods of operations research 46 (1997), S. 281-284 
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
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  • 6
    Title: Plazieren von Zellen: Theorie und Lösung eines quadratischen 0/1- Optimierungsproblems. Zugl. Berlin, Techn. Univ., Diss., 1992; TR 92-3
    Author: Weismantel, Robert
    Publisher: Berlin :Konrad-Zuse-Zentrum,
    Year of publication: 1992
    Pages: 221 S.
    Series Statement: Technical Report TR 92-3
    Type of Medium: Book
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  • 7
    Book
    Book
    Belmont, Mass. :Dynamic Ideas,
    Title: Optimization over integers
    Author: Bertsimas, Dimitris
    Contributer: Weismantel, Robert
    Publisher: Belmont, Mass. :Dynamic Ideas,
    Year of publication: 2005
    ISBN: 0-9759146-2-6
    Type of Medium: Book
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  • 8
    Title: Optimum Path Packing on Wheels: The Noncrossing Case. /; Preprint SC 93-26
    Author: Grötschel, Martin
    Contributer: Martin, Alexander , Weismantel, Robert
    Publisher: Berlin :Konrad-Zuse-Zentrum für Informationstechnik,
    Year of publication: 1993
    Pages: 24 S.
    Series Statement: Preprint / Konrad-Zuse-Zentrum für Informationstechnik Berlin Preprint SC 93-26
    ISSN: 0933-7911
    Type of Medium: Book
    Language: English
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  • 9
    Book
    Book
    Berlin :Konrad-Zuse-Zentrum für Informationstechnik,
    Title: ¬The¬ Sequential Knapsack Polytope /; Preprint SC 94-30
    Author: Pochet, Yves
    Contributer: Weismantel, Robert
    Publisher: Berlin :Konrad-Zuse-Zentrum für Informationstechnik,
    Year of publication: 1994
    Series Statement: Preprint / Konrad-Zuse-Zentrum für Informationstechnik Berlin Preprint SC 94-30
    ISSN: 0933-7911
    Type of Medium: Book
    Language: English
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  • 10
    Title: Some Integer Programs Arising in the Design of Main Frame Computers. /; Preprint SC 92-25
    Author: Ferreira, Carlos E.
    Contributer: Grötschel, Martin , Kiefl, S. , Krispenz, L. , Martin, Alexander , Weismantel, Robert
    Publisher: Berlin :Konrad-Zuse-Zentrum für Informationstechnik,
    Year of publication: 1992
    Pages: 28 S.
    Series Statement: Preprint / Konrad-Zuse-Zentrum für Informationstechnik Berlin Preprint SC 92-25
    ISSN: 0933-7911
    Type of Medium: Book
    Language: English
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