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Interior point methods for solving linearly constrained convex programming involve a variable projection matrix at each iteration to deal with the linear constraints. This matrix often becomes ill-conditioned near the boundary of the…

Optimization and Control · Mathematics 2024-12-31 Xun Qian , Li-Zhi Liao , Jie Sun

We prove that finding a rooted subtree with at least $k$ leaves in a digraph is a fixed parameter tractable problem. A similar result holds for finding rooted spanning trees with many leaves in digraphs from a wide family $\cal L$ that…

Data Structures and Algorithms · Computer Science 2007-05-23 Noga Alon , Fedor Fomin , Gregory Gutin , Michael Krivelevich , Saket Saurabh

A tree decomposition of a graph facilitates computations by grouping vertices into bags that are interconnected in an acyclic structure, hence their importance in a plethora of problems such as query evaluation over databases and inference…

Data Structures and Algorithms · Computer Science 2018-10-09 Noam Ravid , Dori Medini , Benny Kimelfeld

We study the Requirement Cut problem, a generalization of numerous classical graph partitioning problems including Multicut, Multiway Cut, $k$-Cut, and Steiner Multicut among others. Given a graph with edge costs, terminal groups $(S_1,…

Data Structures and Algorithms · Computer Science 2025-11-25 Nadym Mallek , Kirill Simonov

The notions of bounded expansion and nowhere denseness have been applied very successfully in algorithmic graph theory. We study the corresponding notions of directed bounded expansion and nowhere crownfulness on directed graphs. We show…

Discrete Mathematics · Computer Science 2017-07-10 Stephan Kreutzer , Patrice Ossona de Mendez , Roman Rabinovich , Sebastian Siebertz

This paper focuses on parallel hash functions based on tree modes of operation for an inner Variable-Input-Length function. This inner function can be either a single-block-length (SBL) and prefix-free MD hash function, or a sponge-based…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-06-13 Kevin Atighehchi , Robert Rolland

Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views,…

Artificial Intelligence · Computer Science 2017-11-15 Georg Gottlob , Gianlugi Greco , Francesco Scarcello

Given two rooted, ordered, and labeled trees $P$ and $T$ the tree inclusion problem is to determine if $P$ can be obtained from $T$ by deleting nodes in $T$. This problem has recently been recognized as an important query primitive in XML…

Data Structures and Algorithms · Computer Science 2011-01-19 Philip Bille , Inge Li Goertz

Arising from structural graph theory, treewidth has become a focus of study in fixed-parameter tractable algorithms in various communities including combinatorics, integer-linear programming, and numerical analysis. Many NP-hard problems…

Data Structures and Algorithms · Computer Science 2023-09-14 Sally Dong , Yin Tat Lee , Guanghao Ye

We study fundamental problems in linear algebra, such as finding a maximal linearly independent subset of rows or columns (a basis), solving linear regression, or computing a subspace embedding. For these problems, we consider input…

Data Structures and Algorithms · Computer Science 2023-01-20 Yeshwanth Cherapanamjeri , Sandeep Silwal , David P. Woodruff , Samson Zhou

Deep Neural Networks (DNN) have demonstrated superior ability to extract high level embedding vectors from low level features. Despite the success, the serving time is still the bottleneck due to expensive run-time computation of multiple…

Machine Learning · Computer Science 2017-03-16 Jie Zhu , Ying Shan , JC Mao , Dong Yu , Holakou Rahmanian , Yi Zhang

The problem of deciding the validity (QSAT) of quantified Boolean formulas (QBF) is a vivid research area in both theory and practice. In the field of parameterized algorithmics, the well-studied graph measure treewidth turned out to be a…

Computational Complexity · Computer Science 2020-07-06 Johannes Klaus Fichte , Markus Hecher , Andreas Pfandler

Random forests and, more generally, (decision\nobreakdash-)tree ensembles are widely used methods for classification and regression. Recent algorithmic advances allow to compute decision trees that are optimal for various measures such as…

Machine Learning · Computer Science 2024-09-25 Christian Komusiewicz , Pascal Kunz , Frank Sommer , Manuel Sorge

Solving integer programs of the form $\min \{\mathbf{x} \mid A\mathbf{x} = \mathbf{b}, \mathbf{l} \leq \mathbf{x} \leq \mathbf{u}, \mathbf{x} \in \mathbb{Z}^n \}$ is, in general, $\mathsf{NP}$-hard. Hence, great effort has been put into…

Data Structures and Algorithms · Computer Science 2025-10-28 Marcin Briański , Alexandra Lassota , Kristýna Pekárková , Michał Pilipczuk , Janina Reuter

Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of…

Machine Learning · Computer Science 2023-09-28 Xiyang Hu , Cynthia Rudin , Margo Seltzer

Program behavior may depend on parameters, which are either configured before compilation time, or provided at run-time, e.g., by sensors or other input devices. Parametric program analysis explores how different parameter settings may…

Programming Languages · Computer Science 2014-06-23 Thomas M. Gawlitza , Martin D. Schwarz , Helmut Seidl

Dynamic programming on tree decompositions is a frequently used approach to solve otherwise intractable problems on instances of small treewidth. In recent work by Bodlaender et al., it was shown that for many connectivity problems, there…

Data Structures and Algorithms · Computer Science 2013-06-03 Stefan Fafianie , Hans L. Bodlaender , Jesper Nederlof

In 1996, Bodlaender showed the celebrated result that an optimal tree decomposition of a graph of bounded treewidth can be found in linear time. The algorithm is based on an algorithm of Bodlaender and Kloks that computes an optimal tree…

Data Structures and Algorithms · Computer Science 2020-03-19 Ernst Althaus , Sarah Ziegler

The bandwidth of a $n$-vertex graph $G$ is the smallest integer $b$ such that there exists a bijective function $f : V(G) \rightarrow \{1,...,n\}$, called a layout of $G$, such that for every edge $uv \in E(G)$, $|f(u) - f(v)| \leq b$. In…

Data Structures and Algorithms · Computer Science 2014-05-01 Markus Sortland Dregi , Daniel Lokshtanov

Branch-and-cut is the most widely used algorithm for solving integer programs, employed by commercial solvers like CPLEX and Gurobi. Branch-and-cut has a wide variety of tunable parameters that have a huge impact on the size of the search…

Machine Learning · Computer Science 2022-05-13 Maria-Florina Balcan , Siddharth Prasad , Tuomas Sandholm , Ellen Vitercik