MINIMIZATION OF PLANAR DIRECTED ACYCLIC GRAPH ALGEBRAS

2013 ◽  
Vol 24 (04) ◽  
pp. 519-531
Author(s):  
ANTONIOS KALAMPAKAS ◽  
OLYMPIA LOUSCOU-BOZAPALIDOU
Keyword(s):  
Directed Acyclic Graph ◽  
Directed Acyclic Graphs ◽  
Graph Algebras ◽  
Minimization Method ◽  
Nondeterministic Automaton ◽  
Acyclic Graph ◽  
Acyclic Graphs

We introduce planar directed acyclic graph algebras and present an explicit minimization method. The minimal simulation of a nondeterministic automaton on planar directed acyclic graphs is constructed.

scholarly journals Potential Outcome and Directed Acyclic Graph Approaches to Causality: Relevance for Empirical Practice in Economics

2020 ◽  
Vol 58 (4) ◽  
pp. 1129-1179
Author(s):  
Guido W. Imbens
Keyword(s):  
Directed Acyclic Graph ◽  
Empirical Work ◽  
Directed Acyclic Graphs ◽  
Potential Outcome ◽  
Acyclic Graph ◽  
Acyclic Graphs ◽  
Outcome Framework ◽  
Outcome Perspective

In this essay I discuss potential outcome and graphical approaches to causality, and their relevance for empirical work in economics. I review some of the work on directed acyclic graphs, including the recent The Book of Why (Pearl and Mackenzie 2018). I also discuss the potential outcome framework developed by Rubin and coauthors (e.g., Rubin 2006), building on work by Neyman (1990 [1923]). I then discuss the relative merits of these approaches for empirical work in economics, focusing on the questions each framework answers well, and why much of the the work in economics is closer in spirit to the potential outcome perspective. (JEL C31, C36, I26)

scholarly journals Consistency Guarantees for Greedy Permutation-Based Causal Inference Algorithms

Biometrika ◽  
2021 ◽  
Author(s):  
L Solus ◽  
Y Wang ◽  
C Uhler
Keyword(s):  
Graphical Models ◽  
Directed Acyclic Graph ◽  
Real Data ◽  
Directed Acyclic Graphs ◽  
Equivalence Classes ◽  
Acyclic Graph ◽  
Basic Task ◽  
Acyclic Graphs ◽  
Edge Graph ◽  
Markov Equivalence

Abstract Directed acyclic graphical models are widely used to represent complex causal systems. Since the basic task of learning such a model from data is NP-hard, a standard approach is greedy search over the space of directed acyclic graphs or Markov equivalence classes of directed acyclic graphs. As the space of directed acyclic graphs on p nodes and the associated space of Markov equivalence classes are both much larger than the space of permutations, it is desirable to consider permutation-based greedy searches. Here, we provide the first consistency guarantees, both uniform and high-dimensional, of a greedy permutation-based search. This search corresponds to a simplex-like algorithm operating over the edge-graph of a subpolytope of the permutohedron, called a directed acyclic graph associahedron. Every vertex in this polytope is associated with a directed acyclic graph, and hence with a collection of permutations that are consistent with the directed acyclic graph ordering. A walk is performed on the edges of the polytope maximizing the sparsity of the associated directed acyclic graphs. We show via simulated and real data that this permutation search is competitive with current approaches.

scholarly journals Improvement of layered directed acyclic graph layout in CourseViewer

2019 ◽  
Author(s):  
Geovana Marinello Palomo ◽  
Celmar Guimaraes da Silva
Keyword(s):  
Directed Acyclic Graph ◽  
Directed Acyclic Graphs ◽  
Graph Layout ◽  
Acyclic Graph ◽  
Interactive Diagrams ◽  
Edge Crossing ◽  
Acyclic Graphs ◽  
Edge Bundling ◽  
Crossing Minimization

CourseViewer is a software that uses interactive diagrams to assist students, teachers, and course coordinators in analyzing information related to academic transcripts and course curriculum, which are represented as layered directed acyclic graphs of subjects and prerequisites. Recent improvements in the layout of these graphs included edge crossing minimization and better horizontal positioning of nodes. This work continues this list of improvements by means of researching edge bundling techniques that group edges of layered directed acyclic graphs, in order to simplify graph understanding. We selected and implemented an edge bundling technique in CourseViewer. We also exemplify course curricula in which we applied this technique.

scholarly journals A directed acyclic graph for interactions

2020 ◽  
Author(s):  
Anton Nilsson ◽  
Carl Bonander ◽  
Ulf Strömberg ◽  
Jonas Björk
Keyword(s):  
Directed Acyclic Graph ◽  
Causal Effect ◽  
Target Population ◽  
Directed Acyclic Graphs ◽  
Indirect Interaction ◽  
Causal Relationships ◽  
Fundamental Feature ◽  
Acyclic Graph ◽  
Acyclic Graphs ◽  
New Type

Abstract Background Directed acyclic graphs (DAGs) are of great help when researchers try to understand the nature of causal relationships and the consequences of conditioning on different variables. One fundamental feature of causal relations that has not been incorporated into the standard DAG framework is interaction, i.e. when the effect of one variable (on a chosen scale) depends on the value that another variable is set to. In this paper, we propose a new type of DAG—the interaction DAG (IDAG), which can be used to understand this phenomenon. Methods The IDAG works like any DAG but instead of including a node for the outcome, it includes a node for a causal effect. We introduce concepts such as confounded interaction and total, direct and indirect interaction, showing that these can be depicted in ways analogous to how similar concepts are depicted in standard DAGs. This also allows for conclusions on which treatment interactions to account for empirically. Moreover, since generalizability can be compromised in the presence of underlying interactions, the framework can be used to illustrate threats to generalizability and to identify variables to account for in order to make results valid for the target population. Conclusions The IDAG allows for a both intuitive and stringent way of illustrating interactions. It helps to distinguish between causal and non-causal mechanisms behind effect variation. Conclusions about how to empirically estimate interactions can be drawn—as well as conclusions about how to achieve generalizability in contexts where interest lies in estimating an overall effect.

Modeling overlapping structures

2013 ◽  
Author(s):  
Yves Marcoux ◽  
Michael Sperberg-McQueen ◽  
Claus Huitfeldt
Keyword(s):  
Directed Graphs ◽  
Upper Bounds ◽  
Directed Acyclic Graphs ◽  
Markup Language ◽  
Multiple Roots ◽  
Acyclic Graph ◽  
Xml Documents ◽  
Acyclic Graphs ◽  
Structured Document ◽  
Definition Of

The problem of overlapping structures has long been familiar to the structured document community. In a poem, for example, the verse and line structures overlap, and having them both available simultaneously is convenient, and sometimes necessary (for example for automatic analyses). However, only structures that embed nicely can be represented directly in XML. Proposals to address this problem include XML solutions (based essentially on a layer of semantics) and non-XML ones. Among the latter is TexMecs HS2003, a markup language that allows overlap (and many other features). XML documents, when viewed as graphs, correspond to trees. Marcoux M2008 characterized overlap-only TexMecs documents by showing that they correspond exactly to completion-acyclic node-ordered directed acyclic graphs. In this paper, we elaborate on that result in two ways. First, we cast it in the setting of a strictly larger class of graphs, child-arc-ordered directed graphs, that includes multi-graphs and non-acyclic graphs, and show that — somewhat surprisingly — it does not hold in general for graphs with multiple roots. Second, we formulate a stronger condition, full-completion-acyclicity, that guarantees correspondence with an overlap-only document, even for graphs that have multiple roots. The definition of fully-completion-acyclic graph does not in itself suggest an efficient algorithm for checking the condition, nor for computing a corresponding overlap-only document when the condition is satisfied. We present basic polynomial-time upper bounds on the complexity of accomplishing those tasks.

Maintaining Constrained Path Problem for Directed Acyclic Graphs

2021 ◽  
Vol 21 (03) ◽  
Author(s):  
Chenying Hao ◽  
Shurong Zhang ◽  
Weihua Yang
Keyword(s):  
Shortest Path ◽  
Time Complexity ◽  
Directed Acyclic Graph ◽  
Shortest Paths ◽  
Directed Acyclic Graphs ◽  
Shortest Path Algorithm ◽  
Acyclic Graphs ◽  
Main Technique ◽  
Number Formula ◽  
The One

In order to restore the faulty path in network more effectively, we propose the maintaining constrained path problem. Give a directed acyclic graph (DAG) [Formula: see text] with some faulty edges, where [Formula: see text], [Formula: see text]. For any positive number [Formula: see text], we give effective maintain algorithm for finding and maintaining the path between source vertex [Formula: see text] and destination [Formula: see text] with length at most [Formula: see text]. In this paper, we consider the parameters [Formula: see text] and [Formula: see text] which are used to measure the numbers of edges and vertices which are influenced by faulty edges, respectively. The main technique of this paper is to define and solve a subproblem called the one to set constrained path problem (OSCPP) which has not been addressed before. On the DAG, compared with the dynamic shortest path algorithm with time complexity [Formula: see text] [16] and the shortest path algorithm with time complexity [Formula: see text] [18], based on the algorithm for OSCPP, we develop a maintaining constrained path algorithm and improve the time complexity to [Formula: see text] in the case that all shortest paths from each vertex [Formula: see text] to [Formula: see text] have been given.

scholarly journals Phasertng: directed acyclic graphs for crystallographic phasing

2021 ◽  
Vol 77 (1) ◽  
pp. 1-10
Author(s):  
Airlie J. McCoy ◽  
Duncan H. Stockwell ◽  
Massimo D. Sammito ◽  
Robert D. Oeffner ◽  
Kaushik S. Hatti ◽  
...  
Keyword(s):  
Directed Acyclic Graph ◽  
Directed Acyclic Graphs ◽  
Molecular Replacement ◽  
Molecular Fragments ◽  
Graph Data ◽  
Acyclic Graphs ◽  
Structure Solution ◽  
Experimental Phasing ◽  
Graph Management ◽  
Extract Phase

Crystallographic phasing strategies increasingly require the exploration and ranking of many hypotheses about the number, types and positions of atoms, molecules and/or molecular fragments in the unit cell, each with only a small chance of being correct. Accelerating this move has been improvements in phasing methods, which are now able to extract phase information from the placement of very small fragments of structure, from weak experimental phasing signal or from combinations of molecular replacement and experimental phasing information. Describing phasing in terms of a directed acyclic graph allows graph-management software to track and manage the path to structure solution. The crystallographic software supporting the graph data structure must be strictly modular so that nodes in the graph are efficiently generated by the encapsulated functionality. To this end, the development of new software, Phasertng, which uses directed acyclic graphs natively for input/output, has been initiated. In Phasertng, the codebase of Phaser has been rebuilt, with an emphasis on modularity, on scripting, on speed and on continuing algorithm development. As a first application of phasertng, its advantages are demonstrated in the context of phasertng.xtricorder, a tool to analyse and triage merged data in preparation for molecular replacement or experimental phasing. The description of the phasing strategy with directed acyclic graphs is a generalization that extends beyond the functionality of Phasertng, as it can incorporate results from bioinformatics and other crystallographic tools, and will facilitate multifaceted search strategies, dynamic ranking of alternative search pathways and the exploitation of machine learning to further improve phasing strategies.

Propagating Distributions Up Directed Acyclic Graphs

1999 ◽  
Vol 11 (1) ◽  
pp. 215-227 ◽  
Author(s):  
Eric B. Baum ◽  
Warren D. Smith
Keyword(s):  
Graphical Models ◽  
Directed Acyclic Graph ◽  
Search Tree ◽  
Directed Acyclic Graphs ◽  
Game Tree ◽  
Worst Case ◽  
Exponential Time ◽  
Acyclic Graphs ◽  
Game Trees ◽  
Directed Growth

In a previous article, we considered game trees as graphical models. Adopting an evaluation function that returned a probability distribution over values likely to be taken at a given position, we described how to build a model of uncertainty and use it for utility-directed growth of the search tree and for deciding on a move after search was completed. In some games, such as chess and Othello, the same position can occur more than once, collapsing the game tree to a directed acyclic graph (DAG). This induces correlations among the distributions at sibling nodes. This article discusses some issues that arise in extending our algorithms to a DAG. We give a simply described algorithm for correctly propagating distributions up a game DAG, taking account of dependencies induced by the DAG structure. This algorithm is exponential time in the worst case. We prove that it is #P complete to propagate distributions up a game DAG correctly. We suggest how our exact propagation algorithm can yield a fast but inexact heuristic.

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