173 research outputs found
Capturing Topology in Graph Pattern Matching
Graph pattern matching is often defined in terms of subgraph isomorphism, an
NP-complete problem. To lower its complexity, various extensions of graph
simulation have been considered instead. These extensions allow pattern
matching to be conducted in cubic-time. However, they fall short of capturing
the topology of data graphs, i.e., graphs may have a structure drastically
different from pattern graphs they match, and the matches found are often too
large to understand and analyze. To rectify these problems, this paper proposes
a notion of strong simulation, a revision of graph simulation, for graph
pattern matching. (1) We identify a set of criteria for preserving the topology
of graphs matched. We show that strong simulation preserves the topology of
data graphs and finds a bounded number of matches. (2) We show that strong
simulation retains the same complexity as earlier extensions of simulation, by
providing a cubic-time algorithm for computing strong simulation. (3) We
present the locality property of strong simulation, which allows us to
effectively conduct pattern matching on distributed graphs. (4) We
experimentally verify the effectiveness and efficiency of these algorithms,
using real-life data and synthetic data.Comment: VLDB201
Shared Memory Parallel Subgraph Enumeration
The subgraph enumeration problem asks us to find all subgraphs of a target
graph that are isomorphic to a given pattern graph. Determining whether even
one such isomorphic subgraph exists is NP-complete---and therefore finding all
such subgraphs (if they exist) is a time-consuming task. Subgraph enumeration
has applications in many fields, including biochemistry and social networks,
and interestingly the fastest algorithms for solving the problem for
biochemical inputs are sequential. Since they depend on depth-first tree
traversal, an efficient parallelization is far from trivial. Nevertheless,
since important applications produce data sets with increasing difficulty,
parallelism seems beneficial.
We thus present here a shared-memory parallelization of the state-of-the-art
subgraph enumeration algorithms RI and RI-DS (a variant of RI for dense graphs)
by Bonnici et al. [BMC Bioinformatics, 2013]. Our strategy uses work stealing
and our implementation demonstrates a significant speedup on real-world
biochemical data---despite a highly irregular data access pattern. We also
improve RI-DS by pruning the search space better; this further improves the
empirical running times compared to the already highly tuned RI-DS.Comment: 18 pages, 12 figures, To appear at the 7th IEEE Workshop on Parallel
/ Distributed Computing and Optimization (PDCO 2017
Fast Search for Dynamic Multi-Relational Graphs
Acting on time-critical events by processing ever growing social media or
news streams is a major technical challenge. Many of these data sources can be
modeled as multi-relational graphs. Continuous queries or techniques to search
for rare events that typically arise in monitoring applications have been
studied extensively for relational databases. This work is dedicated to answer
the question that emerges naturally: how can we efficiently execute a
continuous query on a dynamic graph? This paper presents an exact subgraph
search algorithm that exploits the temporal characteristics of representative
queries for online news or social media monitoring. The algorithm is based on a
novel data structure called the Subgraph Join Tree (SJ-Tree) that leverages the
structural and semantic characteristics of the underlying multi-relational
graph. The paper concludes with extensive experimentation on several real-world
datasets that demonstrates the validity of this approach.Comment: SIGMOD Workshop on Dynamic Networks Management and Mining (DyNetMM),
201
Expert System for Crop Disease based on Graph Pattern Matching: A proposal
Para la agroindustria, las enfermedades en cultivos constituyen uno de los problemas más frecuentes que generan grandes pérdidas económicas y baja calidad en la producción. Por otro lado, desde las ciencias de la computación, han surgido diferentes herramientas cuya finalidad es mejorar la prevención y el tratamiento de estas enfermedades. En este sentido, investigaciones recientes proponen el desarrollo de sistemas expertos para resolver este problema haciendo uso de técnicas de minería de datos e inteligencia artificial, como inferencia basada en reglas, árboles de decisión, redes bayesianas, entre otras. Además, los grafos pueden ser usados para el almacenamiento de los diferentes tipos de variables que se encuentran presentes en un ambiente de cultivos, permitiendo la aplicación de técnicas de minería de datos en grafos, como el emparejamiento de patrones en los mismos. En este artículo presentamos una visión general de las temáticas mencionadas y una propuesta de un sistema experto para enfermedades en cultivos, basado en emparejamiento de patrones en grafos.For agroindustry, crop diseases constitute one of the most common problems that generate large economic losses and low production quality. On the other hand, from computer science, several tools have emerged in order to improve the prevention and treatment of these diseases. In this sense, recent research proposes the development of expert systems to solve this problem, making use of data mining and artificial intelligence techniques like rule-based inference, decision trees, Bayesian network, among others. Furthermore, graphs can be used for storage of different types of variables that are present in an environment of crops, allowing the application of graph data mining techniques like graph pattern matching. Therefore, in this paper we present an overview of the above issues and a proposal of an expert system for crop disease based on graph pattern matching
PATTERN MATCHING IN METAMODEL-BASED MODEL TRANSFORMATION SYSTEMS
The vision of the OMG´s Model-Driven Architecture (MDA) has
necessitated the extensive research of model compilers, which are able to
process graph-based visual models specified mainly in the Unified Modeling
Language (UML). A possible mechanism for the realization of MDA model
compilers can be graph rewriting-based transformation approach. Previous work
has introduced the tool Visual Modeling and Transformation System, which uses
graph rewriting as transformation mechanism, but the pattern language of
the rewriting rules consists of UML class diagram elements instead of object
diagram level patterns. This paper provides the algorithmic background for the
application of these rules specified by the class diagram elements. To achieve
that, it examines the allowed instantiation configuration based on the UML
standard, and supplies a constructive algorithm to compute the allowed number
of the objects participating in a valid instantiation of a class model.
Furthermore, starting from the VF2 algorithm, the pattern matching algorithm
for the left hand side of the metamodel-based rewriting rule is provided via
several optimization steps examined
Symmetry-Based Quantum Circuit Mapping
Quantum circuit mapping is a crucial process in the quantum circuit
compilation pipeline, facilitating the transformation of a logical quantum
circuit into a list of instructions directly executable on a target quantum
system. Recent research has introduced a post-compilation step known as
remapping, which seeks to reconfigure the initial circuit mapping to mitigate
quantum circuit errors arising from system variability. As quantum processors
continue to scale in size, the efficiency of quantum circuit mapping and the
overall compilation process has become of paramount importance. In this work,
we introduce a quantum circuit remapping algorithm that leverages the intrinsic
symmetries in quantum processors, making it well-suited for large-scale quantum
systems. This algorithm identifies all topologically equivalent circuit
mappings by constraining the search space using symmetries and accelerates the
scoring of each mapping using vector computation. Notably, this symmetry-based
circuit remapping algorithm exhibits linear scaling with the number of qubits
in the target quantum hardware and is proven to be optimal in terms of its time
complexity. Moreover, we conduct a comparative analysis against existing
methods in the literature, demonstrating the superior performance of our
symmetry-based method on state-of-the-art quantum hardware architectures and
highlighting the practical utility of our algorithm, particularly for quantum
processors with millions of qubits.Comment: 10 pages, 5 figures; comments are welcom
Polynomial Algorithm for Submap Isomorphism: Application to searching patterns in images
International audienceIn this paper, we address the problem of searching for a pattern in a plane graph, i.e., a planar drawing of a planar graph. To do that, we propose to model plane graphs with 2-dimensional combinatorial maps, which provide nice data structures for modelling the topology of a subdivision of a plane into nodes, edges and faces. We define submap isomorphism, we give a polynomial algorithm for this problem, and we show how this problem may be used to search for a pattern in a plane graph. First experimental results show the validity of this approach to efficiently search for patterns in images
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