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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
An Implementation of Logical Analysis of Data
An implementation of this "logical analysis of data" (LAD) methodology is described, along with the results of numerical experiments demonstrating the classification performance of LAD in comparison with the reported results of other procedures. Expand
Logical analysis of numerical data
The theoretical foundations of the binarization process studying the combinatorial optimization problems related to the minimization of the number of binary variables are developed and compact linear integer programming formulations of them are constructed. Expand
Preprocessing of unconstrained quadratic binary optimization
It is shown that 100% data reduction is achieved using the proposed preprocessing techniques for MAX-CUT graphs derived from VLSI design, MAX-Clique in c-fat graphsderived from fault diagnosis, and minimum vertex cover problems in random planar graphs of up to 500 000 vertices. Expand
Minimization of Half-Products
It is shown that while the minimization over the set of binary n-vectors for half-products is NP-complete, an e-approximating solution can be found in polynomial time for any e > 0. Expand
On Short Paths Interdiction Problems: Total and Node-Wise Limited Interdiction
It is shown that the short paths node-wise interdiction problem can be efficiently solved by an extension of Dijkstra’s algorithm and the same inapproximability bounds hold for undirected graphs and/or node elimination. Expand
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
Generating All Vertices of a Polyhedron Is Hard
It is shown that generating all negative cycles of a weighted graph is a hard enumeration problem, in both the directed and undirected cases, implying that (directed) negative cycles cannot be generated in polynomial output time, unless P=NP. Expand
Polynomial-time inference of all valid implications for Horn and related formulae
The complexity of a general inference problem: given a propositional formula in conjunctive normal form, find all prime implications of the formula can be solved in time polynomially bounded in the size of the input and in the number of prime implications. Expand
Covering Non-uniform Hypergraphs
A non-trivial upper bound for T(n, F, r) is computed for the maximum possible number of edges in a graph with n vertices, which contains each member of F at most r?1 times. Expand