Peter L. Hammer

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This survey examines the state of the art of a variety of problems related to pseudo-Boolean optimization, i.e. to the optimization of set functions represented by closed algebraic expressions. The main parts of the survey examine general pseudo-Boolean optimization, the specially important case of quadratic pseudo-Boolean optimization (to which every(More)
I Given an mxn zero-one matrix A we ask whether there is a single linear inequality ax ,< b whosi zero-one solutions are precisely the zero-one solutins of "& < e . We develop an algorithm for answering this question in O(mn*) st""eps &d investigate other related problems. Our results may be interpreted in terms of graph theory and threshold logic. f L L i(More)
ÐThe paper describes a new, logic-based methodology for analyzing observations. The key features of the Logical Analysis of Data (LAD) are the discovery of minimal sets of features necessary for explaining all observations and the detection of hidden patterns in the data capable of distinguishing observations describing apositiveo outcome events from(More)
Annals of Mathematics and Artificial Intelligence presents a range of topics of concern to scholars applying quantitative, combinatorial, logical, algebraic and algorithmic methods to diverse areas of Artificial Intelligence, from decision support, automated deduction, and reasoning, to knowledge-based systems, machine learning, computer vision, robotics(More)
This paper studies the approximation of pseudo-Boolean functions by linear functions and more generally by functions of (at most) a specified degree. Here a pseudo-Boolean function means a real valued function defined on {0, 1} n, and its degree is that of the unique multilinear polynomial that expresses it; linear functions are those of degree at most one.(More)
We propose several efficient preprocessing techniques for Unconstrained Quadratic Binary Optimization (QUBO), including the direct use of enhanced versions of known basic techniques (e.g., implications derived from first and second order derivatives and from roof–duality), and the integrated use (e.g., by probing and by consensus) of the basic techniques.(More)