Related papers: An Abstract Model for Branch and Cut
Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…
In the present paper we formally define the notion of abstract program slicing, a general form of program slicing where properties of data are considered instead of their exact value. This approach is applied to a language with numeric and…
Besides serving as prediction models, classification trees are useful for finding important predictor variables and identifying interesting subgroups in the data. These functions can be compromised by weak split selection algorithms that…
Full strong-branching is a well-known variable selection rule that is known experimentally to produce significantly smaller branch-and-bound trees in comparison to all other known variable selection rules. In this paper, we attempt an…
The unmatched ability of Deep Neural Networks in capturing complex patterns in large and noisy datasets is often associated with their large hypothesis space, and consequently to the vast amount of parameters that characterize model…
Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…
Tree-based protocols are ubiquitous in distributed systems. They are flexible, they perform generally well, and, in static conditions, their analysis is mostly simple. Under churn, however, node joins and failures can have complex global…
A decision tree is commonly restricted to use a single hyperplane to split the covariate space at each of its internal nodes. It often requires a large number of nodes to achieve high accuracy, hurting its interpretability. In this paper,…
We examine how recently documented, fundamental phenomena in deep learning models subject to pruning are affected by changes in the pruning procedure. Specifically, we analyze differences in the connectivity structure and learning dynamics…
This paper deals with computation trees over an arbitrary structure consisting of a set along with collections of functions and predicates that are defined on it. It is devoted to the comparative analysis of three parameters of problems…
The multi-modal nature of many vision problems calls for neural network architectures that can perform multiple tasks concurrently. Typically, such architectures have been handcrafted in the literature. However, given the size and…
The branching algorithm is a fundamental technique for designing fast exponential-time algorithms to solve combinatorial optimization problems exactly. It divides the entire solution space into independent search branches using…
Regression trees have emerged as a preeminent tool for solving real-world regression problems due to their ability to deal with nonlinearities, interaction effects and sharp discontinuities. In this article, we rather study regression trees…
In connection with the needs of solving optimization problems, the development of conditional minimization methods with convenient numerical implementation continues to attract the attention of mathematicians. In this monograph we propose…
This paper presents and evaluates two pruning techniques to reinforce the efficiency of constraint optimization solvers based on multi-valued decision-diagrams (MDD). It adopts the branch-and-bound framework proposed by Bergman et al. in…
Branch prediction is a standard feature in most processors, significantly improving the run time of programs by allowing a processor to predict the direction of a branch before it has been evaluated. Current branch prediction methods can…
Robust optimization is one of the fundamental approaches to deal with uncertainty in combinatorial optimization. This paper considers the robust spanning tree problem with interval data, which arises in a variety of telecommunication…
We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling…
In branching simulation, a novel approach to simulation presented in this paper, a multiplicity of plausible scenarios are concurrently developed and implemented. In conventional simulations of complex systems, there arise from time to time…
While many classes of cutting-planes are at the disposal of integer programming solvers, our scientific understanding is far from complete with regards to cutting-plane selection, i.e., the task of selecting a portfolio of cutting-planes to…