Growing Graphs with Hyperedge Replacement Graph Grammars

Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. In this paper we show that a graph's clique tree can be used to extract a hyperedge replacement grammar. If we store an ordering from the extraction process, the extracted graph grammar is guaranteed to generate an isomorphic copy of the original graph. Or, a stochastic application of the graph grammar rules can be used to quickly create random graphs. In experiments on large real world networks, we show that random graphs, generated from extracted graph grammars, exhibit a wide range of properties that are very similar to the original graphs. In addition to graph properties like degree or eigenvector centrality, what a graph "looks like" ultimately depends on small details in local graph substructures that are difficult to define at a global level. We show that our generative graph model is able to preserve these local substructures when generating new graphs and performs well on new and difficult tests of model robustness.Comment: 18 pages, 19 figures, accepted to CIKM 2016 in Indianapolis, I

Parsing of Hyperedge Replacement Grammars with Graph Parser Combinators

Graph parsing is known to be computationally expensive. For this reason the construction of special-purpose parsers may be beneficial for particular graph languages. In the domain of string languages so-called parser combinators are very popular for writing efficient parsers. Inspired by this approach, we have proposed graph parser combinators in a recent paper, a framework for the rapid development of special-purpose graph parsers. Our basic idea has been to define primitive graph parsers for elementary graph components and a set of combinators for the flexible construction of more advanced graph parsers. Following this approach, a declarative, but also more operational description of a graph language can be given that is a parser at the same time. In this paper we address the question how the process of writing correct parsers on top of our framework can be simplified by demonstrating the translation of hyperedge replacement grammars into graph parsers. The result are recursive descent parsers as known from string parsing with some additional nondeterminism

Exploiting the Layout Engine to Assess Diagram Completions

A practicable approach to diagram completion is to first compute model completions on the abstract syntax level. These can be translated to corresponding diagram changes by the layout engine afterwards. Normally, several different model completions are possible though. One way to deal with this issue is to let the user choose among them explicitly, which is already helpful. However, such a choice step is a quite time-consuming interruption of the editing process. We argue that users often are mainly interested in completions that preserve their original diagram as far as possible. This criterion cannot be checked on the abstract syntax level though. In fact, minimal model changes might still result in enormous changes of the original diagram. Therefore, we suggest to use the layout engine in advance for assessing all possible model completions with respect to the diagram changes they eventually cause

Hypergrammar-based parallel multi-frontal solver for grids with point singularities

This paper describes the application of hypergraph grammars to drive linear computationalcost solver for grids with point singularities. Such graph grammar productions are the rstmathematical formalism used to describe solver algorithm and each of them indicates thesmallest atomic task that can be executed in parallel, which is very useful in case of parallelexecution. In particular the partial order of execution of graph grammar productions can befound, and the sets of independent graph grammar productions can be localized. They canbe scheduled set by set into shared memory parallel machine. The graph grammar basedsolver has been implemented with NIVIDIA CUDA for GPU. Graph grammar productionsare accompanied by numerical results for 2D case. We show that our graph grammar basedsolver with GPU accelerator is order of magnitude faster than state of the art MUMPSsolver

Layout Specification on the Concrete and Abstract Syntax Level of a Diagram Language

A visual language consists of several visual component types, e.g. states or transitions in DFAs. Nowadays, the language itself is usually specified via a meta model. To make a diagram look nice, a layouter is required. This layouter may either operate on the concrete syntax level, i.e., on the visual components, or on the abstract syntax level, i.e., on the model instance. In this paper we present an approach that is capable of specifying a flexible layout on both, the concrete as well as the abstract syntax level of a diagram. The approach uses pattern-based transformations. Besides structured editing, it also supports free-hand editing, a challenging task for the layouter. We introduce how such a specification can be created and examine the advantages and shortcomings of each of either operating on the concrete syntax level or on the abstract syntax level

Applications of a hyper-graph grammar system in adaptive finite-element computations

This paper describes application of a hyper-graph grammar system for modeling a three-dimensional adaptive finite element method. The hyper-graph grammar approach allows obtaining a linear computational cost of adaptive mesh transformations and computations performed over refined meshes. The computations are done by a hyper-graph grammar driven algorithm applicable to three-dimensional problems. For the case of typical refinements performed towards a point or an edge, the algorithm yields linear computational cost with respect to the mesh nodes for its sequential execution and logarithmic cost for its parallel execution. Such hyper-graph grammar productions are the mathematical formalism used to describe the computational algorithm implementing the finite element method. Each production indicates the smallest atomic task that can be executed concurrently. The mesh transformations and computations by using the hyper-graph grammar-based approach have been tested in the GALOIS environment. We conclude the paper with some numerical results performed on a shared-memory Linux cluster node, for the case of three-dimensional computational meshes refined towards a point, an edge and a face

A Combinatorial Framework for Designing (Pseudoknotted) RNA Algorithms

We extend an hypergraph representation, introduced by Finkelstein and Roytberg, to unify dynamic programming algorithms in the context of RNA folding with pseudoknots. Classic applications of RNA dynamic programming energy minimization, partition function, base-pair probabilities...) are reformulated within this framework, giving rise to very simple algorithms. This reformulation allows one to conceptually detach the conformation space/energy model -- captured by the hypergraph model -- from the specific application, assuming unambiguity of the decomposition. To ensure the latter property, we propose a new combinatorial methodology based on generating functions. We extend the set of generic applications by proposing an exact algorithm for extracting generalized moments in weighted distribution, generalizing a prior contribution by Miklos and al. Finally, we illustrate our full-fledged programme on three exemplary conformation spaces (secondary structures, Akutsu's simple type pseudoknots and kissing hairpins). This readily gives sets of algorithms that are either novel or have complexity comparable to classic implementations for minimization and Boltzmann ensemble applications of dynamic programming

Graph design by graph grammar evolution

Singapor