BioJS DAGViewer: A reusable JavaScript component for displaying directed graphs

Summary: The DAGViewer BioJS component is a reusable JavaScript component made available as part of the BioJS project and intended to be used to display graphs of structured data, with a particular emphasis on Directed Acyclic Graphs (DAGs). It enables users to embed representations of graphs of data, such as ontologies or phylogenetic trees, in hyper-text documents (HTML). This component is generic, since it is capable (given the appropriate configuration) of displaying any kind of data that is organised as a graph. The features of this component which are useful for examining and filtering large and complex graphs are described.Availability: http://github.com/alexkalderimis/dag-viewer-biojs; http://github.com/biojs/biojs; http://dx.doi.org/10.5281/zenodo.8303.

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Parameterized Complexity of Directed Spanner Problems

Algorithmica ◽

10.1007/s00453-021-00911-x ◽

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.

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Modeling overlapping structures

Proceedings of Balisage: The Markup Conference 2013 ◽

10.4242/balisagevol10.marcoux01 ◽

2013 ◽

Cited By ~ 7

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.

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Probabilistic Directed Acyclic Graphs and Their Entropies

Pattern Theory ◽

10.1093/oso/9780198505709.003.0004 ◽

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.

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Display Sets of Normal and Tree-Child Networks

The Electronic Journal of Combinatorics ◽

10.37236/9128 ◽

2021 ◽

Vol 28 (1) ◽

Author(s):

Janosch Döcker ◽

Simone Linz ◽

Charles Semple

Keyword(s):

Decision Problem ◽

Phylogenetic Trees ◽

Phylogenetic Network ◽

Polynomial Time Algorithm ◽

Time Algorithm ◽

Directed Acyclic Graphs ◽

Phylogenetic Networks ◽

Acyclic Graphs ◽

Normal Network ◽

Normal Networks

Phylogenetic networks are leaf-labelled directed acyclic graphs that are used in computational biology to analyse and represent the evolutionary relationships of a set of species or viruses. In contrast to phylogenetic trees, phylogenetic networks have vertices of in-degree at least two that represent reticulation events such as hybridisation, lateral gene transfer, or reassortment. By systematically deleting various combinations of arcs in a phylogenetic network $\mathcal N$, one derives a set of phylogenetic trees that are embedded in $\mathcal N$. We recently showed that the problem of deciding if two binary phylogenetic networks embed the same set of phylogenetic trees is computationally hard, in particular, we showed it to be $\Pi^P_2$-complete. In this paper, we establish a polynomial-time algorithm for this decision problem if the initial two networks consist of a normal network and a tree-child network; two well-studied topologically restricted subclasses of phylogenetic networks, with normal networks being more structurally constrained than tree-child networks. The running time of the algorithm is quadratic in the size of the leaf sets.

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Cooperative Control for Uncertain Multiagent Systems via Distributed Output Regulation

Mathematical Problems in Engineering ◽

10.1155/2013/898375 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Lu Yu ◽

Jinzhi Wang

Keyword(s):

Multiagent Systems ◽

Cooperative Control ◽

Controller Design ◽

Directed Graphs ◽

Directed Acyclic Graphs ◽

Output Regulation ◽

Feedback Controller ◽

Dynamic State ◽

Linear Matrix ◽

Acyclic Graphs

The distributed robust output regulation problem for multiagent systems is considered. For heterogeneous uncertain linear systems and a linear exosystem, the controlling aim is to stabilize the closed-loop system and meanwhile let the regulated outputs converge to the origin asymptotically, by the help of local interaction. The communication topology considered is directed acyclic graphs, which means directed graphs without loops. With distributed dynamic state feedback controller and output feedback controller, respectively, the solvability of the problem and the algorithm of controller design are both investigated. The solvability conditions are given in terms of linear matrix inequalities (LMIs). It is shown that, for polytopic uncertainties, the distributed controllers constructed by solving LMIs can satisfy the requirements of output regulation property.

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