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See detailThe Mathematics of Peter L. Hammer (1936-2006): Graphs, Optimization, and Boolean Models
Boros, Endre; Crama, Yves ULiege; De Werra, Dominique et al

in Boros, Endre; Crama, Yves; De Werra, Dominique (Eds.) et al The Mathematics of Peter L. Hammer (1936-2006): Graphs, Optimization, and Boolean Models (2011)

This volume of the Annals of Operations Research, contains a collection of papers published in memory of Peter L. Hammer. As we recall further down, Peter made substantial contributions to several areas ... [more ▼]

This volume of the Annals of Operations Research, contains a collection of papers published in memory of Peter L. Hammer. As we recall further down, Peter made substantial contributions to several areas of operations research and discretemathematics, including, in particular, mathematical programming (linear and quadratic 0–1 programming, pseudo-Boolean optimization, knapsack problems, etc.), combinatorial optimization (transportation problems, network flows, MAXSAT, simple plant location, etc.), graph theory (special classes of graphs, stability problems, and their applications), data mining and classification (Logical Analysis of Data), and, last but not least, Boolean theory (satisfiability, duality, Horn functions, threshold functions, and their applications). [less ▲]

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See detailThe Mathematics of Peter L. Hammer (1936-2006): Graphs, Optimization, and Boolean Models
Boros, Endre; Crama, Yves ULiege; de Werra, Dominique et al

in Annals of Operations Research (2011), 188

This volume contains a collection of papers published in memory of Peter L. Hammer (1936-2006). Peter Hammer made substantial contributions to several areas of operations research and discrete mathematics ... [more ▼]

This volume contains a collection of papers published in memory of Peter L. Hammer (1936-2006). Peter Hammer made substantial contributions to several areas of operations research and discrete mathematics, including, in particular, mathematical programming (linear and quadratic 0--1 programming, pseudo-Boolean optimization, knapsack problems, etc.), combinatorial optimization (transportation problems, network flows, MAXSAT, simple plant location, etc.), graph theory (special classes of graphs, stability problems, and their applications), data mining and classification (Logical Analysis of Data), and, last but not least, Boolean theory (satisfiability, duality, Horn functions, threshold functions, and their applications). The volume contains 23 contributed papers along these lines. [less ▲]

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See detailComplexity of product positioning and ball intersection problems
Crama, Yves ULiege; Hansen, Pierre; Jaumard, Brigitte

in Mathematics of Operations Research (1995), 20

The product positioning problem consists in choosing the attributes of a new product in such a way as to maximize its market share, i.e., to attract a maximum number of customers. Mathematically, the ... [more ▼]

The product positioning problem consists in choosing the attributes of a new product in such a way as to maximize its market share, i.e., to attract a maximum number of customers. Mathematically, the problem can be formulated as follows: given a set of balls (with respect to some norm) and a weight associated to each ball, find a point which maximizes the sum of the weights of the balls containing it. The complexity of this problem is investigated in the case of the L∞ and of the Euclidean norms. In both cases, the problem is proved to be NP-hard, but to be polynomially solvable when the dimension of the space is fixed. [less ▲]

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See detailDetection of spurious states of neural networks
Crama, Yves ULiege; Hansen, Pierre; Jaumard, Brigitte

in IEEE Transactions on Neural Networks (1991), 2

The authors study the complexity and propose an algorithm for the problem of determining, given p vectors of {-1,1}^n, all linear combinations of them which are also in {-1,1}^n. Computational results are ... [more ▼]

The authors study the complexity and propose an algorithm for the problem of determining, given p vectors of {-1,1}^n, all linear combinations of them which are also in {-1,1}^n. Computational results are reported. This problem corresponds to the detection of spurious states in neural networks. [less ▲]

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See detailThe basic algorithm for pseudo-Boolean programming revisited
Crama, Yves ULiege; Hansen, Pierre; Jaumard, Brigitte

in Discrete Applied Mathematics (1990), 29

The basic algorithm of pseudo-Boolean programming due to Hammer and Rudeanu allows to minimize nonlinear 0–1 functions by recursively eliminating one variable at each iteration. We show it has linear-time ... [more ▼]

The basic algorithm of pseudo-Boolean programming due to Hammer and Rudeanu allows to minimize nonlinear 0–1 functions by recursively eliminating one variable at each iteration. We show it has linear-time complexity when applied to functions associated in a natural way with graphs of bounded tree-width. We also propose a new approach to the elimination of a variable based on a branch-and-bound scheme, which allows shortcuts in Boolean manipulations. Computational results are reported on. [less ▲]

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See detailAn introduction to the ELECTRE research programme
Crama, Yves ULiege; Hansen, Pierre

in Hansen, Pierre (Ed.) Essays and Surveys on Multiple Criteria Decision Making (1983)

The discrete multicriteria decision problem has attracted a large amount of attention during the last 15 years. In contrast with multi-attribute utility theory, prevailing in the U.S., a series of methods ... [more ▼]

The discrete multicriteria decision problem has attracted a large amount of attention during the last 15 years. In contrast with multi-attribute utility theory, prevailing in the U.S., a series of methods have been developped in Europe, mostly by Roy and his co-workers, under the name ELECTRE. The present paper is devoted to an overview of that research programme. [less ▲]

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