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Directed acyclic graph (DAG) learning is a central task in structure discovery and causal inference. Although the field has witnessed remarkable advances over the past few years, it remains statistically and computationally challenging to…

Machine Learning · Statistics 2026-02-09 Ryan Thompson , Edwin V. Bonilla , Robert Kohn

The \textsc{Degree Realization} problem with respect to a graph family $\mathcal{F}$ is defined as follows. The input is a sequence $d$ of $n$ positive integers, and the goal is to decide whether there exists a graph $G \in \mathcal{F}$…

Discrete Mathematics · Computer Science 2025-09-09 Amotz Bar-Noy , Toni Bohnlein , David Peleg , Yingli Ran , Dror Rawitz

Nonlinear matrix equations arise in many practical contexts related to control theory, dynamical programming and finite element methods for solving some partial differential equations. In most of these applications, it is needed to compute…

Numerical Analysis · Mathematics 2014-10-22 Negin Bagherpour , Nezam Mahdavi-Amiri

We study the following fundamental realization problem of directed acyclic graphs (dags). Given a sequence S:=(a_1,b_1),...,(a_n, b_n) with a_i, b_i in Z_0^+, does there exist a dag (no parallel arcs allowed) with labeled vertex set V:=…

Data Structures and Algorithms · Computer Science 2012-03-19 Annabell Berger , Matthias Müller-Hannemann

A partial complement of the graph $G$ is a graph obtained from $G$ by complementing all the edges in one of its induced subgraphs. We study the following algorithmic question: for a given graph $G$ and graph class $\mathcal{G}$, is there a…

Computational Complexity · Computer Science 2020-06-11 Fedor V. Fomin , Petr A. Golovach , Torstein J. F. Strømme , Dimitrios M. Thilikos

We consider the problem of constructing distribution-free prediction sets with finite-sample conditional guarantees. Prior work has shown that it is impossible to provide exact conditional coverage universally in finite samples. Thus, most…

Methodology · Statistics 2024-09-18 Isaac Gibbs , John J. Cherian , Emmanuel J. Candès

We call a topological ordering of a weighted directed acyclic graph non-negative if the sum of weights on the vertices in any prefix of the ordering is non-negative. We investigate two processes for constructing non-negative topological…

Combinatorics · Mathematics 2016-09-21 Dániel Gerbner , Balázs Keszegh , Cory Palmer , Dömötör Pálvölgyi

We give a signed generalization of Laurent's theorem that characterizes feasible positive semidefinite matrix completion problems in terms of metric polytopes. Based on this result, we give a characterization of the maximum rank completions…

Combinatorics · Mathematics 2016-04-04 Shin-ichi Tanigawa

In some applications of matching, the structural or hierarchical properties of the two graphs being aligned must be maintained. The hierarchical properties are induced by the direction of the edges in the two directed graphs. These…

Data Structures and Algorithms · Computer Science 2009-09-29 Sean M. Falconer , Dmitri Maslov

This work addresses the NP-Hard problem of acyclic directed acyclic graph (DAG) partitioning problem. The acyclic partitioning problem is defined as partitioning the vertex set of a given directed acyclic graph into disjoint and…

Data Structures and Algorithms · Computer Science 2022-07-28 M. Yusuf Özkaya , Ümit V. Çatalyürek

Precise knowledge of causal directed acyclic graphs (DAGs) is assumed for standard approaches towards valid adjustment set selection for unbiased estimation, but in practice, the DAG is often inferred from data or expert knowledge,…

Statistics Theory · Mathematics 2025-11-14 Zhongyi Hu , Stéphanie van der Pas

In observational studies, the true causal model is typically unknown and needs to be estimated from available observational and limited experimental data. In such cases, the learned causal model is commonly represented as a partially…

Artificial Intelligence · Computer Science 2023-03-01 Malte Luttermann , Marcel Wienöbst , Maciej Liśkiewicz

Directed acyclic graphs (DAGs) are directed graphs in which there is no path from a vertex to itself. DAGs are an omnipresent data structure in computer science and the problem of counting the DAGs of given number of vertices and to sample…

Discrete Mathematics · Computer Science 2025-10-03 Martin Pépin , Alfredo Viola

We propose a numerical method, based on the shift-and-invert power iteration, that answers whether a symmetric matrix is positive definite ("yes") or not ("no"). Our method uses randomization. But, it returns the correct answer with high…

Numerical Analysis · Mathematics 2018-06-27 Martin Neuenhofen

Directed acyclic graphs (DAGs) are a class of graphs commonly used in practice, with examples that include electronic circuits, Bayesian networks, and neural architectures. While many effective encoders exist for DAGs, it remains…

Machine Learning · Computer Science 2025-05-30 Michael Sun , Orion Foo , Gang Liu , Wojciech Matusik , Jie Chen

A real symmetric matrix $A$ is said to be completely positive if it can be written as $BB^t$ for some (not necessarily square) nonnegative matrix $B$. A simple graph $G$ is called a completely positive graph if every doubly nonnegative…

Combinatorics · Mathematics 2020-02-07 Joyentanuj Das , Sachindranath Jayaraman , Sumit Mohanty

A polynomial-time exact algorithm for counting the number of directed acyclic graphs in a Markov equivalence class was recently given by Wien\"obst, Bannach, and Li\'skiewicz (AAAI 2021). In this paper, we consider the more general problem…

Data Structures and Algorithms · Computer Science 2023-06-14 Vidya Sagar Sharma

We investigate the odd multiway node (edge) cut problem where the input is a graph with a specified collection of terminal nodes and the goal is to find a smallest subset of nonterminal nodes (edges) to delete so that the terminal nodes do…

Data Structures and Algorithms · Computer Science 2018-04-09 Karthekeyan Chandrasekaran , Matthias Mnich , Sahand Mozaffari

The complexity of graph homomorphism problems has been the subject of intense study. It is a long standing open problem to give a (decidable) complexity dichotomy theorem for the partition function of directed graph homomorphisms. In this…

Computational Complexity · Computer Science 2010-08-06 Jin-Yi Cai , Xi Chen

We study the perfect matching reconfiguration problem: Given two perfect matchings of a graph, is there a sequence of flip operations that transforms one into the other? Here, a flip operation exchanges the edges in an alternating cycle of…

Data Structures and Algorithms · Computer Science 2019-04-15 Marthe Bonamy , Nicolas Bousquet , Marc Heinrich , Takehiro Ito , Yusuke Kobayashi , Arnaud Mary , Moritz Mühlenthaler , Kunihiro Wasa