1,720,978 research outputs found
On a generalization of the Chvátal–Gomory closure
No full text© 2021, Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society.Many practical integer programming problems involve variables with one or two-sided bounds. Dunkel and Schulz (A refined Gomory–Chvátal closure for polytopes in the unit cube, http://www.optimization-online.org/DB_FILE/2012/03/3404.pdf, 2012) considered a strengthened version of Chvátal–Gomory (CG) inequalities that use 0–1 bounds on variables, and showed that the set of points in a rational polytope that satisfy all these strengthened inequalities is a polytope. Recently, we generalized this result by considering strengthened CG inequalities that use all variable bounds. In this paper, we generalize further by considering not just variable bounds, but general linear constraints on variables. We show that all points in a rational polyhedron that satisfy such strengthened CG inequalities form a rational polyhedron. We also extend this polyhedrality result to mixed-integer sets defined by linear constraints.11Nsciescopu
On a Generalization of the Chvátal-Gomory Closure
No full textMany practical integer programming problems involve variables with one or two-sided bounds. Dunkel and Schulz (2012) considered a strengthened version of Chvátal-Gomory (CG) inequalities that use 0–1 bounds on variables, and showed that the set of points in a rational polytope that satisfy all these strengthened inequalities is a polytope. Recently, we generalized this result by considering strengthened CG inequalities that use all variable bounds. In this paper, we generalize further by considering not just variable bounds, but general linear constraints on variables. We show that all points in a rational polyhedron that satisfy such strengthened CG inequalities form a rational polyhedron. © 2020, Springer Nature Switzerland AG
Generalized Chvatal-Gomory closures for integer programs with bounds on variables
No full textInteger programming problems that arise in practice often involve decision variables with one or two sided bounds. In this paper, we consider a generalization of Chvatal-Gomory inequalities obtained by strengthening Chvatal-Gomory inequalities using the bounds on the variables. We prove that the closure of a rational polyhedron obtained after applying the generalized Chvatal-Gomory inequalities is also a rational polyhedron. This generalizes a result of Dunkel and Schulz on 0-1 problems to the case when some of the variables have upper or lower bounds or both while the rest of them are unbounded.11Nsciescopu
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
On the matrix cuts of Lovasz and Schrijver and their use in integer programming
No full textAn important approach to solving many discrete optimization problems is to associate the discrete set (over which we wish to optimize) with the 0-1 vectors in a given polyhedron and to derive linear inequalities valid for these 0-1 vectors from a linear inequality system defining the polyhedron. Lovasz and Schrijver (1991) described a family of operators, called the matrix-cut operators, which generate strong valid inequalities, called matrix cuts, for the 0-1 vectors in a polyhedron. This family includes the commutative, semidefinite and division operators; each operator can be applied iteratively to obtain, in n iterations for polyhedra in n-space, the convex hull of 0-1 vectors.
We study the complexity of matrix-cut based methods for solving 0-1 integer linear programs. We first prove bounds on the (rank) number of iterations required to obtain the integer hull. We show that the upper bound of n, mentioned above, can be attained in the case of the semidefinite operator, answering a question of Goemans. We also determine the semidefinite rank of the standard linear relaxation of the traveling salesman polytope up to a constant factor. We study the use of the semidefinite operator in solving numerical instances and present results on some combinatorial examples and also on a few instances from the MIPLIB test set. Finally, we examine the lengths of cutting-plane proofs based on matrix cuts. We answer a question of Pudlak on such proofs, and prove an exponential lower bound on the length of cutting-plane proofs based on one class of matrix cuts
On the Matrix Cuts of Lovász and Schrijver and Their Use in Integer Programming
No full textThis work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/17952An important approach to solving many discrete optimization problems is to associate the discrete set (over which we wish to optimize) with the 0-1 vectors in a given polyhedron and to derive linear inequalities valid for these 0-1 vectors from a linear inequality system defining the polyhedron. Lovász and Schrijver (1991) described a family of operators, called the matrix-cut operators, which generate strong valid inequalities, called matrix cuts, forthe 0-1 vectors in a polyhedron. This family includes the commutative, semidefinite and division operators; each operator can be applied iteratively to obtain, in n iterations for polyhedra in n-space, the convex hull of 0-1 vectors. We study the complexity of matrix-cut based methods for solving 0-1 integer linear programs. We first prove bounds on the (rank) number of iterations required to obtain the integer hull. We show that the upper bound of n, mentioned above, can be attained in the case of the semidefinite operator, answering a question of Goemans. We also determine the semidefinite rank of the standard linear relaxation of the traveling salesman polytope up to a constant factor. We study the use of the semidefinite operator in solving numerical instances and present results on some combinatorial examples and also on a few instances from the MIPLIB test set. Finally, we examine the lengths of cutting-plane proofs based on matrix cuts. We answer a question of Pudlák on such proofs, and prove an exponential lower bound on the length of cutting-plane proofs based on one class of matrix cuts
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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