Results 1  10
of
31
THetA: Inferring intratumor heterogeneity from highthroughput DNA sequencing data
, 2013
"... ..."
The ChvátalGomory Closure of a Strictly Convex Body
"... In this paper, we prove that the Ch´vatalGomory closure of a set obtained as an intersection of a strictly convex body and a rational polyhedron is a polyhedron. Thus, we generalize a result of Schrijver[29] which shows that the Ch´vatalGomory closure of a rational polyhedron is a polyhedron. Key ..."
Abstract

Cited by 13 (6 self)
 Add to MetaCart
(Show Context)
In this paper, we prove that the Ch´vatalGomory closure of a set obtained as an intersection of a strictly convex body and a rational polyhedron is a polyhedron. Thus, we generalize a result of Schrijver[29] which shows that the Ch´vatalGomory closure of a rational polyhedron is a polyhedron. Key words: nonlinear integer programming; cutting planes; Ch´vatalGomory closure
An effective branchandbound algorithm for convex quadratic integer programming
 Math. Program
, 2012
"... We present a branchandbound algorithm for minimizing a convex quadratic objective function over integer variables subject to convex constraints. In a given node of the enumeration tree, corresponding to the fixing of a subset of the variables, a lower bound is given by the continuous minimum of th ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
(Show Context)
We present a branchandbound algorithm for minimizing a convex quadratic objective function over integer variables subject to convex constraints. In a given node of the enumeration tree, corresponding to the fixing of a subset of the variables, a lower bound is given by the continuous minimum of the restricted objective function. We improve this bound by exploiting the integrality of the variables using suitablydefined latticefree ellipsoids. Experiments show that our approach is very fast on both unconstrained problems and problems with box constraints. The main reason is that all expensive calculations can be done in a preprocessing phase, while a single node in the enumeration tree can be processed in linear time in the problem dimension. 1
COMBINATORICS AND GEOMETRY OF TRANSPORTATION POLYTOPES: AN UPDATE
, 2013
"... A transportation polytope consists of all multidimensional arrays or tables of nonnegative real numbers that satisfy certain sum conditions on subsets of the entries. They arise naturally in optimization and statistics, and also have interest for discrete mathematics because permutation matrices, ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
A transportation polytope consists of all multidimensional arrays or tables of nonnegative real numbers that satisfy certain sum conditions on subsets of the entries. They arise naturally in optimization and statistics, and also have interest for discrete mathematics because permutation matrices, latin squares, and magic squares appear naturally as lattice points of these polytopes. In this paper we survey advances on the understanding of the combinatorics and geometry of these polyhedra and include some recent unpublished results on the diameter of graphs of these polytopes. In particular, this is a thirtyyear update on the status of a list of open questions last visited in the 1984 book by Yemelichev, Kovalev and Kravtsov and the 1986 survey paper of Vlach.
nFold integer programming in cubic time
, 2013
"... nFold integer programming is a fundamental problem with a variety of natural applications in operations research and statistics. Moreover, it is universal and provides a new, variabledimension, parametrization of all of integer programming. The fastest algorithm for nfold integer programming pr ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
nFold integer programming is a fundamental problem with a variety of natural applications in operations research and statistics. Moreover, it is universal and provides a new, variabledimension, parametrization of all of integer programming. The fastest algorithm for nfold integer programming predating the present article runs in time O ng(A)L with L the binary length of the numerical part of the input and g(A) the socalled Graver complexity of the bimatrix A defining the system. In this article we provide a drastic improvement and establish an algorithm which runs in time O n3L having cubic dependency on n regardless of the bimatrix A. Our algorithm works for separable convex piecewise affine objectives as well. Moreover, it can be used to define a hierarchy of approximations for any integer programming problem.
A Lower Bound for the Graver Complexity of the Incidence Matrix of a Complete Bipartite Graph
, 2011
"... ..."
GRAVER BASIS AND PROXIMITY TECHNIQUES FOR BLOCKSTRUCTURED SEPARABLE CONVEX INTEGER MINIMIZATION PROBLEMS
"... ar ..."
(Show Context)
Scalable Test Data Generation from Multidimensional Models
"... Multidimensional data models form the core of modern decision support software. The need for this kind of software is significant, and it continues to grow with the size and variety of datasets being collected today. Yet real multidimensional instances are often unavailable for testing and benchmark ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Multidimensional data models form the core of modern decision support software. The need for this kind of software is significant, and it continues to grow with the size and variety of datasets being collected today. Yet real multidimensional instances are often unavailable for testing and benchmarking, and existing data generators can only produce a limited class of such structures. In this paper, we present a new framework for scalable generation of test data from a rich class of multidimensional models. The framework provides a small, expressive language for specifying such models, and a novel solver for generating sample data from them. While the satisfiability problem for the language is NPhard, we identify a polynomially solvable fragment that captures most practical modeling patterns. Given a model and, optionally, a statistical specification of the desired test dataset, the solver detects and instantiates a maximal subset of the model within this fragment, generating data that exhibits the desired statistical properties. We use our framework to generate a variety of highquality test datasets from real industrial models, which cannot be correctly instantiated by existing data generators, or as effectively solved by generalpurpose constraint solvers.