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.

scholarly journals Fully Dynamic Transitive Closure in Plane Dags with one Source and one Sink

1994 ◽  
Vol 1 (30) ◽  
Author(s):  
Thore Husfeldt
Keyword(s):  
Transitive Closure ◽  
Upper Bounds ◽  
Directed Acyclic Graphs ◽  
Closure Problem ◽  
Directed Path ◽  
Lower And Upper Bounds ◽  
New Techniques ◽  
Time Dynamic ◽  
Acyclic Graphs ◽  
Closure Algorithm

We give an algorithm for the Dynamic Transitive Closure Problem for planar directed acyclic graphs with one source and one sink. The graph can be updated in logarithmic time under arbitrary edge insertions and deletions that preserve the embedding. Queries of the form `is there a directed path from u to v ?' for arbitrary vertices u and v can be answered in logarithmic time. The size of the data structure and the initialisation time are linear in the number of edges.<br /> <br />The result enlarges the class of graphs for which a logarithmic (or even polylogarithmic) time dynamic transitive closure algorithm exists. Previously, the only algorithms within the stated resource bounds put restrictions on the topology of the graph or on the delete operation. To obtain our result, we use a new characterisation of the transitive closure in plane graphs with one source and one sink and introduce new techniques to exploit this characterisation.<br /> <br />We also give a lower bound of Omega(log n/log log n) on the amortised complexity of the problem in the cell probe model with logarithmic word size. This is the first dynamic directed graph problem with almost matching lower and upper bounds.

scholarly journals Parameterized Complexity of Directed Spanner Problems

Algorithmica ◽  
2021 ◽  
Author(s):  
Fedor V. Fomin ◽  
Petr A. Golovach ◽  
William Lochet ◽  
Pranabendu Misra ◽  
Saket Saurabh ◽  
...  
Keyword(s):  
Directed Graph ◽  
Parameterized Complexity ◽  
Directed Graphs ◽  
Directed Acyclic Graphs ◽  
Polynomial Kernel ◽  
Distortion Parameter ◽  
Spanning Subgraph ◽  
Acyclic Graphs ◽  
Positive Integers ◽  
Additive Distortion

AbstractWe initiate the parameterized complexity study of minimum t-spanner problems on directed graphs. For a positive integer t, a multiplicative t-spanner of a (directed) graph G is a spanning subgraph H such that the distance between any two vertices in H is at most t times the distance between these vertices in G, that is, H keeps the distances in G up to the distortion (or stretch) factor t. An additive t-spanner is defined as a spanning subgraph that keeps the distances up to the additive distortion parameter t, that is, the distances in H and G differ by at most t. The task of Directed Multiplicative Spanner is, given a directed graph G with m arcs and positive integers t and k, decide whether G has a multiplicative t-spanner with at most $$m-k$$ m - k arcs. Similarly, Directed Additive Spanner asks whether G has an additive t-spanner with at most $$m-k$$ m - k arcs. We show that (i) Directed Multiplicative Spanner admits a polynomial kernel of size $$\mathcal {O}(k^4t^5)$$ O ( k 4 t 5 ) and can be solved in randomized $$(4t)^k\cdot n^{\mathcal {O}(1)}$$ ( 4 t ) k · n O ( 1 ) time, (ii) the weighted variant of Directed Multiplicative Spanner can be solved in $$k^{2k}\cdot n^{\mathcal {O}(1)}$$ k 2 k · n O ( 1 ) time on directed acyclic graphs, (iii) Directed Additive Spanner is $${{\,\mathrm{\mathsf{W}}\,}}[1]$$ W [ 1 ] -hard when parameterized by k for every fixed $$t\ge 1$$ t ≥ 1 even when the input graphs are restricted to be directed acyclic graphs. The latter claim contrasts with the recent result of Kobayashi from STACS 2020 that the problem for undirected graphs is $${{\,\mathrm{\mathsf{FPT}}\,}}$$ FPT when parameterized by t and k.

scholarly journals CAUSAL ANALYSIS AFTER HAAVELMO

2014 ◽  
Vol 31 (1) ◽  
pp. 115-151 ◽  
Author(s):  
James Heckman ◽  
Rodrigo Pinto
Keyword(s):  
Economic Models ◽  
Causal Analysis ◽  
Directed Acyclic Graphs ◽  
Ceteris Paribus ◽  
Acyclic Graphs ◽  
Rigorous Treatment ◽  
Definition Of

Haavelmo’s seminal 1943 and 1944 papers are the first rigorous treatment of causality. In them, he distinguished the definition of causal parameters from their identification. He showed that causal parameters are defined usinghypotheticalmodels that assign variation to some of the inputs determining outcomes while holding all other inputs fixed. He thus formalized and made operational Marshall’s (1890)ceteris paribusanalysis. We embed Haavelmo’s framework into the recursive framework of Directed Acyclic Graphs (DAGs) commonly used in the literature of causality (Pearl, 2000) and Bayesian nets (Lauritzen, 1996). We compare the analysis of causality based on a methodology inspired by Haavelmo’s ideas with other approaches used in the causal literature of DAGs. We discuss the limitations of methods that solely use the information expressed in DAGs for the identification of economic models. We extend our framework to consider models for simultaneous causality, a central contribution of Haavelmo.

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)

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.

Probabilistic Directed Acyclic Graphs and Their Entropies

2006 ◽  
Author(s):  
Ulf Grenander ◽  
Michael I. Miller
Keyword(s):  
Markov Chain ◽  
Branching Process ◽  
Directed Graphs ◽  
Directed Acyclic Graphs ◽  
Acyclic Graphs ◽  
Probabilistic Structure

Probabilistic structures on the representations allow for expressing the variation of natural patterns. In this chapter the structure imposed through probabilistic directed graphs is studied. The essential probabilistic structure enforced through the directedness of the graphs is sites are conditionally independent of their nondescendants given their parents. The entropies and combinatorics of these processes are examined as well. Focus is given to the classical Markov chain and the branching process examples to illustrate the fundamentals of variability descriptions through probability and entropy.

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 "Toward a Clearer Definition of Confounding" Revisited With Directed Acyclic Graphs

2012 ◽  
Vol 176 (6) ◽  
pp. 506-511 ◽  
Author(s):  
P. P. Howards ◽  
E. F. Schisterman ◽  
C. Poole ◽  
J. S. Kaufman ◽  
C. R. Weinberg
Keyword(s):  
Directed Acyclic Graphs ◽  
Acyclic Graphs ◽  
Definition Of

scholarly journals Oropharyngeal Dysphagia: A Proposal for an Ecological Theoretical Model

2022 ◽  
pp. 7-16
Author(s):  
Rafaela Soares Rech ◽  
Bárbara Niegia Garcia de Goulart
Keyword(s):  
Data Analysis ◽  
Theoretical Model ◽  
Oropharyngeal Dysphagia ◽  
Theoretical Models ◽  
Epidemiological Studies ◽  
Directed Acyclic Graphs ◽  
Acyclic Graphs ◽  
Confounding Variables ◽  
Direct Causation ◽  
Definition Of

Background: The exponential growth in epidemiological studies has been reflected in an increase in analytical studies. Thus, theoretical models are required to guide the definition of data analysis, although so far, they are seldom used in Speech, Language, and Hearing Sciences. Objective: To propose a multicausal model for oropharyngeal dysphagia using directed acyclic graphs showing mediating variables, confounding variables, and variables connected by direct causation. Design: This integrative literature review. Setting: This was carried out until January 4, 2021, and searches were performed with the MEDLINE, EMBASE,and other bases.

scholarly journals Decision-Theoretic Foundations for Causal Reasoning

1995 ◽  
Vol 3 ◽  
pp. 405-430 ◽  
Author(s):  
D. Heckerman ◽  
R. Shachter
Keyword(s):  
Canonical Form ◽  
Special Class ◽  
Causal Reasoning ◽  
Directed Acyclic Graphs ◽  
Influence Diagrams ◽  
Counterfactual Reasoning ◽  
Cause And Effect ◽  
Acyclic Graphs ◽  
Definition Of ◽  
Theoretic Foundations

We present a definition of cause and effect in terms of decision-theoretic primitives and thereby provide a principled foundation for causal reasoning. Our definition departs from the traditional view of causation in that causal assertions may vary with the set of decisions available. We argue that this approach provides added clarity to the notion of cause. Also in this paper, we examine the encoding of causal relationships in directed acyclic graphs. We describe a special class of influence diagrams, those in canonical form, and show its relationship to Pearl's representation of cause and effect. Finally, we show how canonical form facilitates counterfactual reasoning.

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