Real world datasets may be continuous. Many data analysis algorithms work efficiently on discrete data while some other algorithms work only on discrete data. Thus the continuous datasets are discretized as a pre-process step to knowledge acquisition. Attribute discretization is the process of reducing the domain of a continuous attribute with irreducible and optimal set of cuts, while preservi...

Split cuts are among the most important and well-understood cuts for general mixed-integer programs. In this paper we consider some recent generalizations of split cuts and compare their relative strength. More precisely, we compare the elementary closures of split, cross, crooked cross and general multi-branch split cuts as well as cuts obtained from multi-row and basic relaxations. We present...

 Most debates about the role of tariff cuts on the level of employment and rate of wages in labor market have come out of well-known Hecscher – Ohlin and Stopler – Samuelson (HOS) theorems. Considering the fact that we have divided the workforce into skilled and unskilled labors the present paper assesses the impacts of tariff cuts on labor market indicators in Iran. To address these issues...

The purpose of this paper is to present an overview of families of cutting planes for mixed integer programming problems. We examine the families of disjunctive inequalities, split cuts, mixed integer rounding inequalities, mixed integer Gomory cuts, intersection cuts, lift-and-project cuts, and reduceand-split cuts. In practice, mixed integer Gomory cuts are very useful in obtaining solutions ...

This paper provides a new explanation of why price reductions take place on a regular basis. It is argued that the demand for a ...rm’s product drops over time because of the erosion of consumers’ brand recall, which in turn can be boosted by price cuts. After analyzing the dynamic optimal choice of price discounts in both monopoly and duopoly settings, I show that a monopolist’s optimal pricin...

A basic problem in molecular biology is to rebuild phylogenetic trees from a set of DNA or protein sequences. Among different criteria used for this purpose, the minimum evolution criterion is an optimality based criterion aiming to rebuild phylogenetic trees characterized by a minimal length. This problem is known to be NP-hard. We introduce in this paper some mixed integer programming models,...

Noise in multi-criteria data sets can manifest itself as non-monotonicity. Work on the remediation of such non-monotonicity is rather scarce. Nevertheless, errors are often present in real-life data sets, and several monotone classification algorithms are unable to use such partially non-monotone data sets. Fortunately, as we will show here, it is possible to restore monotonicity in an optimal ...

The notion of the Laplacian of weighted graphs will be introduced, the eigenvectors belonging to k consecutive eigen-values of which define optimal k-dimensional Euclidean representation of the vertices. By means of these spectral techniques some combinatorial problems concerning minimal (k+ 1)-cuts of weighted graphs can be handled easily with linear algebraic tools. (Here k is an arbitrary in...

In a recent paper, Dash, Dey and Günlük (2010) showed that many families of inequalities for the two-row continuous group relaxation and variants of this relaxation are cross cuts or crooked cross cuts, both of which generalize split cuts. Li and Richard (2008) recently studied t-branch split cuts for mixedinteger programs for integers t ≥ 1. Split cuts are just 1-branch split cuts, and cross c...