Tootfinder

This https://arxiv.org/abs/2211.04732 has been replaced.
link: https://scholar.google.com/scholar?q=a

Directed Acyclic Outerplanar Graphs Have Constant Stack Number
The stack number of a directed acyclic graph $G$ is the minimum $k$ for which there is a topological ordering of $G$ and a $k$-coloring of the edges such that no two edges of the same color cross, i.e., have alternating endpoints along the topological ordering. We prove that the stack number of directed acyclic outerplanar graphs is bounded by a constant, which gives a positive answer to a conjecture by Heath, Pemmaraju and Trenk [SIAM J. Computing, 1999]. As an immediate consequence, this show…

This https://arxiv.org/abs/2111.12387 has been replaced.
link: https://scholar.google.com/scholar?q=a

Acyclic reorientation lattices and their lattice quotients
We prove that the acyclic reorientation poset of a directed acyclic graph $D$ is a lattice if and only if the transitive reduction of any induced subgraph of $D$ is a forest. We then show that the acyclic reorientation lattice is always congruence normal, semidistributive (thus congruence uniform) if and only if $D$ is filled, and distributive if and only if $D$ is a forest. When the acyclic reorientation lattice is semidistributive, we introduce the ropes of $D$ that encode the join irreducibl…

HoLens: A Visual Analytics Design for Higher-order Movement Modeling and Visualization
Zezheng Feng, Fang Zhu, Hongjun Wang, Jianing Hao, ShuangHua Yang, Wei Zeng, Huamin Qu
https://arxiv.org/abs/2403.03822

HoLens: A Visual Analytics Design for Higher-order Movement Modeling and Visualization
Higher-order patterns reveal sequential multistep state transitions, which are usually superior to origin-destination analysis, which depicts only first-order geospatial movement patterns. Conventional methods for higher-order movement modeling first construct a directed acyclic graph (DAG) of movements, then extract higher-order patterns from the DAG. However, DAG-based methods heavily rely on the identification of movement keypoints that are challenging for sparse movements and fail to consid…

This https://arxiv.org/abs/2203.01896 has been replaced.
link: https://scholar.google.com/scholar?q=a

Triangulations of Flow Polytopes, Ample Framings, and Gentle Algebras
The cone of nonnegative flows for a directed acyclic graph (DAG) is known to admit regular unimodular triangulations induced by framings of the DAG. These triangulations restrict to triangulations of the flow polytope for strength one flows, which are called DKK triangulations. For a special class of framings called ample framings, these triangulations of the flow cone project to a complete fan. We characterize the DAGs that admit ample framings, and we enumerate the number of ample framings fo…

This https://arxiv.org/abs/2404.01022 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the Complexity of Minimizing Energy Consumption of Partitioning DAG Tasks
We study a graph partition problem where we are given a directed acyclic graph (DAG) whose vertices and arcs can be respectively regarded as tasks and dependencies among tasks. The objective of the problem is to minimize the total energy consumed for completing these tasks by assigning the tasks to k heterogeneous machines. We first show that the problem is NP-hard. Then, we present polynomial-time algorithms for two special cases where there are only two machines and where the input DAG is a d…

MultiFun-DAG: Multivariate Functional Directed Acyclic Graph
Tian Lan, Ziyue Li, Junpeng Lin, Zhishuai Li, Lei Bai, Man Li, Fugee Tsung, Rui Zhao, Chen Zhang
https://arxiv.org/abs/2404.13836

MultiFun-DAG: Multivariate Functional Directed Acyclic Graph
Directed Acyclic Graphical (DAG) models efficiently formulate causal relationships in complex systems. Traditional DAGs assume nodes to be scalar variables, characterizing complex systems under a facile and oversimplified form. This paper considers that nodes can be multivariate functional data and thus proposes a multivariate functional DAG (MultiFun-DAG). It constructs a hidden bilinear multivariate function-to-function regression to describe the causal relationships between different nodes. …

This https://arxiv.org/abs/2310.15627 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Contextual Directed Acyclic Graphs
Estimating the structure of directed acyclic graphs (DAGs) from observational data remains a significant challenge in machine learning. Most research in this area concentrates on learning a single DAG for the entire population. This paper considers an alternative setting where the graph structure varies across individuals based on available "contextual" features. We tackle this contextual DAG problem via a neural network that maps the contextual features to a DAG, represented as a weighted adja…

Exact and Heuristic Computation of the Scanwidth of Directed Acyclic Graphs
Niels Holtgrefe, Leo van Iersel, Mark Jones
https://arxiv.org/abs/2403.12734 ht…

Exact and Heuristic Computation of the Scanwidth of Directed Acyclic Graphs
To measure the tree-likeness of a directed acyclic graph (DAG), a new width parameter that considers the directions of the arcs was recently introduced: scanwidth. We present the first algorithm that efficiently computes the exact scanwidth of general DAGs. For DAGs with one root and scanwidth $k$ it runs in $O(k \cdot n^k \cdot m)$ time. The algorithm also functions as an FPT algorithm with complexity $O(2^{4 \ell - 1} \cdot \ell \cdot n + n^2)$ for phylogenetic networks of level-$\ell$, a typ…

Decentralized Federated Unlearning on Blockchain
Xiao Liu, Mingyuan Li, Xu Wang, Guangsheng Yu, Wei Ni, Lixiang Li, Haipeng Peng, Renping Liu
https://arxiv.org/abs/2402.16294

Decentralized Federated Unlearning on Blockchain
Blockchained Federated Learning (FL) has been gaining traction for ensuring the integrity and traceability of FL processes. Blockchained FL involves participants training models locally with their data and subsequently publishing the models on the blockchain, forming a Directed Acyclic Graph (DAG)-like inheritance structure that represents the model relationship. However, this particular DAG-based structure presents challenges in updating models with sensitive data, due to the complexity and ov…

MultiFun-DAG: Multivariate Functional Directed Acyclic Graph
Tian Lan, Ziyue Li, Junpeng Lin, Zhishuai Li, Lei Bai, Man Li, Fugee Tsung, Rui Zhao, Chen Zhang
https://arxiv.org/abs/2404.13836

MultiFun-DAG: Multivariate Functional Directed Acyclic Graph
Directed Acyclic Graphical (DAG) models efficiently formulate causal relationships in complex systems. Traditional DAGs assume nodes to be scalar variables, characterizing complex systems under a facile and oversimplified form. This paper considers that nodes can be multivariate functional data and thus proposes a multivariate functional DAG (MultiFun-DAG). It constructs a hidden bilinear multivariate function-to-function regression to describe the causal relationships between different nodes. …

Parameterized Task Graph Scheduling Algorithm for Comparing Algorithmic Components
Jared Coleman, Ravi Vivek Agrawal, Ebrahim Hirani, Bhaskar Krishnamachari
https://arxiv.org/abs/2403.07112

Parameterized Task Graph Scheduling Algorithm for Comparing Algorithmic Components
Scheduling distributed applications modeled as directed, acyclic task graphs to run on heterogeneous compute networks is a fundamental (NP-Hard) problem in distributed computing for which many heuristic algorithms have been proposed over the past decades. Many of these algorithms fall under the list-scheduling paradigm, whereby the algorithm first computes priorities for the tasks and then schedules them greedily to the compute node that minimizes some cost function. Thus, many algorithms diffe…

Extending identifiability results from isolated networks to embedded networks
Eduardo Mapurunga, Michel Gevers, Alexandre S. Bazanella
https://arxiv.org/abs/2402.14144

Extending identifiability results from isolated networks to embedded networks
This paper deals with the design of Excitation and Measurement Patterns (EMPs) for the identification of dynamical networks, when the objective is to identify only a subnetwork embedded in a larger network. Recent results have shown how to construct EMPs that guarantee identifiability for a range of networks with specific graph topologies, such as trees, loops, or Directed Acyclic Graphs (DAGs). However, an EMP that is valid for the identification of a subnetwork taken in isolation may no longe…

Causal Orthogonalization: Multicollinearity, Economic Interpretability, and the Gram-Schmidt Process
Robin M. Cross, Steven T. Buccola
https://arxiv.org/abs/2402.17103

Causal Orthogonalization: Multicollinearity, Economic Interpretability, and the Gram-Schmidt Process
This paper considers the problem of interpreting orthogonalization model coefficients. We derive a causal economic interpretation of the Gram-Schmidt orthogonalization process and provide the conditions for its equivalence to total effects from a recursive Directed Acyclic Graph. We extend the Gram-Schmidt process to groups of simultaneous regressors common in economic data sets and derive its finite sample properties, finding its coefficients to be unbiased, stable, and more efficient than tho…

Product of Tensors and Description of Networks
Luca Chiantini, Giuseppe Alessio D'Inverno, Sara Marziali
https://arxiv.org/abs/2402.06768 https://

Product of Tensors and Description of Networks
Any kind of network can be naturally represented by a Directed Acyclic Graph (DAG); additionally, activation functions can determine the reaction of each node of the network with respect to the signal(s) incoming. We study the characterization of the signal distribution in a network under the lens of tensor algebra. More specifically, we describe every activation function as tensor distributions with respect to the nodes, called \textit{activation tensors}. The distribution of the signal is enc…

What Is a Causal Graph?
Philip Dawid
https://arxiv.org/abs/2402.09429 https://arxiv.org/pdf/2402.09429…

What Is a Causal Graph?
This article surveys the variety of ways in which a directed acyclic graph (DAG) can be used to represent a problem of probabilistic causality. For each of these we describe the relevant formal or informal semantics governing that representation. It is suggested that the cleanest such representation is that embodied in an augmented DAG, which contains nodes for non-stochastic intervention indicators in addition to the usual nodes for domain variables.

A Novel Energy-Efficient Cross-Layer Design for Scheduling and Routing in 6TiSCH Networks
Ahlam Hannachi, Wael Jaafar, Salim Bitam, Nabil Ouazene
https://arxiv.org/abs/2403.12949 …

A Novel Energy-Efficient Cross-Layer Design for Scheduling and Routing in 6TiSCH Networks
The 6TiSCH protocol stack was proposed to ensure high-performance communications in the Industrial Internet of Things (IIoT). However, the lack of sufficient time slots for nodes outside the 6TiSCH's Destination Oriented Directed Acyclic Graph (DODAG) to transmit their Destination Advertisement Object (DAO) messages and cell reservation requests significantly hinders their integration into the DODAG. This oversight not only prolongs the device's join time but also increases energy consumption d…

This https://arxiv.org/abs/2310.06881 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qbi…

CAFA-evaluator: A Python Tool for Benchmarking Ontological Classification Methods
We present CAFA-evaluator, a powerful Python program designed to evaluate the performance of prediction methods on targets with hierarchical concept dependencies. It generalizes multi-label evaluation to modern ontologies where the prediction targets are drawn from a directed acyclic graph and achieves high efficiency by leveraging matrix computation and topological sorting. The program requirements include a small number of standard Python libraries, making CAFA-evaluator easy to maintain. The…

A Novel Energy-Efficient Cross-Layer Design for Scheduling and Routing in 6TiSCH Networks
Ahlam Hannachi, Wael Jaafar, Salim Bitam, Nabil Ouazene
https://arxiv.org/abs/2403.12949 …

A Novel Energy-Efficient Cross-Layer Design for Scheduling and Routing in 6TiSCH Networks
The 6TiSCH protocol stack was proposed to ensure high-performance communications in the Industrial Internet of Things (IIoT). However, the lack of sufficient time slots for nodes outside the 6TiSCH's Destination Oriented Directed Acyclic Graph (DODAG) to transmit their Destination Advertisement Object (DAO) messages and cell reservation requests significantly hinders their integration into the DODAG. This oversight not only prolongs the device's join time but also increases energy consumption d…

This https://arxiv.org/abs/2302.14834 has been replaced.
link: https://scholar.google.com/scholar?q=a

DAG-Inducing Problems and Algorithms
Consider the execution of a sequential algorithm that requires the program to converge to an optimal state, and then terminate/stutter. To design such an algorithm, we need to ensure that the state space that it traverses forms a directed acyclic graph (DAG) and its sink nodes are optimal states. However, if we run the same algorithm on multiple computing nodes running in parallel, and without synchronization, it may not reach an optimal state. In most parallel processing algorithms designed in…

This https://arxiv.org/abs/2311.06458 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Conditional Adjustment in a Markov Equivalence Class
We consider the problem of identifying a conditional causal effect through covariate adjustment. We focus on the setting where the causal graph is known up to one of two types of graphs: a maximally oriented partially directed acyclic graph (MPDAG) or a partial ancestral graph (PAG). Both MPDAGs and PAGs represent equivalence classes of possible underlying causal models. After defining adjustment sets in this setting, we provide a necessary and sufficient graphical criterion -- the conditional …

This https://arxiv.org/abs/2309.07080 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qbi…

Discovering Dynamic Effective Connectome of Brain with Bayesian Dynamic DAG Learning
Understanding the complex mechanisms of the brain can be unraveled by extracting the Dynamic Effective Connectome (DEC). Recently, score-based Directed Acyclic Graph (DAG) discovery methods have shown significant improvements in extracting the causal structure and inferring effective connectivity. However, learning DEC through these methods still faces two main challenges: one with the fundamental impotence of high-dimensional dynamic DAG discovery methods and the other with the low quality of …

This https://arxiv.org/abs/2307.04446 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Bounding the chromatic number of dense digraphs by arc neighborhoods
The chromatic number of a directed graph is the minimum number of induced acyclic subdigraphs that cover its vertex set, and accordingly, the chromatic number of a tournament is the minimum number of transitive subtournaments that cover its vertex set. The neighborhood of an arc $uv$ in a tournament $T$ is the set of vertices that form a directed triangle with arc $uv$. We show that if the neighborhood of every arc in a tournament has bounded chromatic number, then the whole tournament has boun…

Asymptotics of relaxed $k$-ary trees
Manosij Ghosh Dastidar, Michael Wallner
https://arxiv.org/abs/2404.08415 https://arxiv.org/pdf/2…

Asymptotics of relaxed $k$-ary trees
A relaxed $k$-ary tree is an ordered directed acyclic graph with a unique source and sink in which every node has out-degree $k$. These objects arise in the compression of trees in which some repeated subtrees are factored and repeated appearances are replaced by pointers. We prove an asymptotic theta-result for the number of relaxed $k$-ary tree with $n$ nodes for $n \to \infty$. This generalizes the previously proved binary case to arbitrary finite arity, and shows that the seldom observed ph…

This https://arxiv.org/abs/2309.07080 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qbi…

Discovering Dynamic Effective Connectome of Brain with Bayesian Dynamic DAG Learning
Understanding the complex mechanisms of the brain can be unraveled by extracting the Dynamic Effective Connectome (DEC). Recently, score-based Directed Acyclic Graph (DAG) discovery methods have shown significant improvements in extracting the causal structure and inferring effective connectivity. However, learning DEC through these methods still faces two main challenges: one with the fundamental impotence of high-dimensional dynamic DAG discovery methods and the other with the low quality of …

Generalized Criterion for Identifiability of Additive Noise Models Using Majorization
Aramayis Dallakyan, Yang Ni
https://arxiv.org/abs/2404.05148 https://…

Generalized Criterion for Identifiability of Additive Noise Models Using Majorization
The discovery of causal relationships from observational data is very challenging. Many recent approaches rely on complexity or uncertainty concepts to impose constraints on probability distributions, aiming to identify specific classes of directed acyclic graph (DAG) models. In this paper, we introduce a novel identifiability criterion for DAGs that places constraints on the conditional variances of additive noise models. We demonstrate that this criterion extends and generalizes existing iden…