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See detailThe Mathematics of Peter L. Hammer (1936-2006): Graphs, Optimization, and Boolean Models
Boros, Endre; Crama, Yves ULg; 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 ULg; 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 ULg; 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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