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Pseudo-Boolean optimization
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. TheExpand
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An Implementation of Logical Analysis of Data
Describes a new, logic-based methodology for analyzing observations. The key features of this "logical analysis of data" (LAD) methodology are the discovery of minimal sets of features that areExpand
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Logical analysis of numerical data
Abstract“Logical analysis of data” (LAD) is a methodology developed since the late eighties, aimed at discovering hidden structural information in data sets. LAD was originally developed forExpand
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Minimization of Half-Products
In this paper a special class of quadratic functions, the so called half-products are considered. It is shown that while the minimization over the set of binary n-vectors for half-products isExpand
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Preprocessing of unconstrained quadratic binary optimization
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.,Expand
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Generating All Vertices of a Polyhedron Is Hard
We show that generating all negative cycles of a weighted graph is a hard enumeration problem, in both the directed and undirected cases. More precisely, given a family of negative (directed) cycles,Expand
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On Short Paths Interdiction Problems: Total and Node-Wise Limited Interdiction
Abstract Given a directed graph G=(V,A) with a non-negative weight (length) function on its arcs w:A→ℝ+ and two terminals s,t∈V, our goal is to destroy all short directed paths from s to t in G byExpand
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The number of triangles covering the center of an n-set
Let the points P1, P2, ..., Pnbe given in the plane such that there are no three on a line. Then there exists a point of the plane which is contained in at least n3/27 (open) PiPjPktriangles. ThisExpand
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Error-Free and Best-Fit Extensions of Partially Defined Boolean Functions
Abstract In this paper, we address a fundamental problem related to the induction of Boolean logic: Given a set of data, represented as a set of binary “truen-vectors” (or “positive examples”) and aExpand
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Polynomial-time inference of all valid implications for Horn and related formulae
This paper investigates the complexity of a general inference problem: given a propositional formula in conjunctive normal form, find all prime implications of the formula. Here, a prime implicationExpand
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