Subgraph Isomorphism Research Articles

A Graph Based Image Interpretation Method Using A Priori Qualitative Inclusion and Photometric Relationships.

This paper presents a method for recovering and identifying image regions from an initial oversegmentation using qualitative knowledge of its content. Compared to recent works favoring spatial information and quantitative techniques, our approach focuses on simple a priori qualitative inclusion and photometric relationships such as "region A is included in region B", "the intensity of region A is lower than the one of region B" or "regions A and B depict similar intensities" (photometric uncertainty). The proposed method is based on a two steps' inexact graph matching approach. The first step searches for the best subgraph isomorphism candidate between expected regions and a subset of regions resulting from the initial oversegmentation. Then, remaining segmented regions are progressively merged with appropriate already matched regions, while preserving the coherence with a priori declared relationships. Strengths and weaknesses of the method are studied on various images (grayscale and color), with various intial oversegmentation algorithms (k-means, meanshift, quickshift). Results show the potential of the method to recover, in a reasonable runtime, expected regions, a priori described in a qualitative manner. For further evaluation and comparison purposes, a Python opensource package implementing the method is provided, together with the specifically built experimental database.

Efficiently detecting structural design pattern instances based on ordered sequences

In software engineering, a design pattern is a general reusable solution to a commonly occurring problem within a given context in software design. Design patterns reveal much about the high-level abstract designs of software systems. Accurately discovering design pattern instances in software systems helps developers and maintainers to understand the original design and implementation, and to facilitate the re-development, upgrade and maintenance. In recent years, numerous approaches have been proposed to discover design pattern instances from system source code. Among them, many transform the source code and design patterns into graphs, and then discover the isomorphic sub-graphs of design patterns from the graph of software system. However, as testing sub-graph isomorphism is an NP-complete problem, those approaches usually fail to achieve satisfactory efficiency. On the other hand, a real time response of detecting pattern instance is in fact essential. To address this problem, we propose a novel efficient approach to detect structural design pattern instances based on directed sub-graph isomorphism. In particular, we put forward a well-designed search order, or Ordered Sequences, by which the candidate pattern instances can be rapidly detected. Because the Ordered Sequences guide the search process in such an order that the most representative classes are discovered first, a large number of irrelevant classes can be filtered out at early stage, which greatly reduces the search space. We employ our approach on four well-known open-source systems. The results of extensive experiments for discovering instances of all GoF structural design patterns verify that our approach obtains 100% recall and the high precision. In addition, the experiment conducted on two other large scale open-source projects indicates that our approach runs significantly faster than the compared approach.

Mining frequent subgraphs in multigraphs

For more than a decade, extracting frequent patterns from single large graphs has been one of the research focuses. However, in this era of data eruption, rich and complex data is being generated at an unprecedented rate. This complex data can be represented as a multigraph structure - a generic and rich graph representation. In this paper, we propose a novel frequent subgraph mining approach MuGraM that can be applied to multigraphs. MuGraM is a generic frequent subgraph mining algorithm that discovers frequent multigraph patterns. MuGraM efficiently performs the task of subgraph matching, which is crucial for support measure, and further leverages several optimization techniques for swift discovery of frequent subgraphs. Our experiments reveal two things: MuGraM discovers multigraph patterns, where other existing approaches are unable to do so; MuGraM, when applied to simple graphs, outperforms the state of the art approaches by at least one order of magnitude.

Counting motifs in dynamic networks

BackgroundA network motif is a sub-network that occurs frequently in a given network. Detection of such motifs is important since they uncover functions and local properties of the given biological network. Finding motifs is however a computationally challenging task as it requires solving the costly subgraph isomorphism problem. Moreover, the topology of biological networks change over time. These changing networks are called dynamic biological networks. As the network evolves, frequency of each motif in the network also changes. Computing the frequency of a given motif from scratch in a dynamic network as the network topology evolves is infeasible, particularly for large and fast evolving networks.ResultsIn this article, we design and develop a scalable method for counting the number of motifs in a dynamic biological network. Our method incrementally updates the frequency of each motif as the underlying network’s topology evolves. Our experiments demonstrate that our method can update the frequency of each motif in orders of magnitude faster than counting the motif embeddings every time the network changes. If the network evolves more frequently, the margin with which our method outperforms the existing static methods, increases.ConclusionsWe evaluated our method extensively using synthetic and real datasets, and show that our method is highly accurate(≥ 96%) and that it can be scaled to large dense networks. The results on real data demonstrate the utility of our method in revealing interesting insights on the evolution of biological processes.

When Subgraph Isomorphism is Really Hard, and Why This Matters for Graph Databases

The subgraph isomorphism problem involves deciding whether a copy of a pattern graph occurs inside a larger target graph. The non-induced version allows extra edges in the target, whilst the induced version does not. Although both variants are NP-complete, algorithms inspired by constraint programming can operate comfortably on many real-world problem instances with thousands of vertices. However, they cannot handle arbitrary instances of this size. We show how to generate "really hard" random instances for subgraph isomorphism problems, which are computationally challenging with a couple of hundred vertices in the target, and only twenty pattern vertices. For the non-induced version of the problem, these instances lie on a satisfiable / unsatisfiable phase transition, whose location we can predict; for the induced variant, much richer behaviour is observed, and constrainedness gives a better measure of difficulty than does proximity to a phase transition. These results have practical consequences: we explain why the widely researched "filter / verify" indexing technique used in graph databases is founded upon a misunderstanding of the empirical hardness of NP-complete problems, and cannot be beneficial when paired with any reasonable subgraph isomorphism algorithm.

Identification of a novel selective small-molecule inhibitor of protein arginine methyltransferase 5 (PRMT5) by virtual screening, resynthesis and biological evaluations

As one of the most promising anticancer target in protein arginine methyltransferase (PRMT) family, PRMT5 has been drawing more and more attentions, and many efforts have been devoted to develop its inhibitors. In this study, three PRMT5 inhibitors (9, 16, and 23) with novel scaffolds were identified by performing pharmacophore- and docking-based virtual screening combined with in vitro radiometric-based scintillation proximity assay (SPA). Substructure search based on the scaffold of the most active 9 afforded 26 additional analogues, and SPA results indicated that two analogues (9–1 and 9–2) showed increased PRMT5 inhibitory activity compared with the parental compound. Resynthesis of 9, 9–1, and 9–2 confirmed their PRMT5 enzymatic inhibition activity. In addition, compound 9–1 displayed selectivity against PRMT5 over other key homological members (PRMT1 and CARM1 (PRMT4)). While the structure–activity relationship (SAR) of this series of compounds was discussed to provide clues for further structure optimization, the probable binding modes of active compounds were also probed by molecular docking and molecular dynamics simulations. Finally, the antiproliferative effect of 9–1 on MV4-11 leukemia cell line was confirmed and its impact on regulating the target gene of PRMT5 was also validated. The hit compounds identified in this work have provided more novel scaffolds for future hit-to-lead optimization of small-molecule PRMT5 inhibitors.

VF2++—An improved subgraph isomorphism algorithm

This paper presents a largely improved version of the VF2 algorithm for the Subgraph Isomorphism Problem. The improvements are twofold. Firstly, it is based on a new approach for determining the matching order of the nodes, and secondly, more efficient — nevertheless easier to compute — cutting rules are proposed. They together reduce the search space significantly.In addition to the usual Subgraph Isomorphism Problem, the paper also presents specialized algorithms for the Induced Subgraph Isomorphism and for the Graph Isomorphism Problems.Finally, an extensive experimental evaluation is provided using a wide range of inputs, including both real-life biological and chemical datasets and standard randomly generated graph series. The results show major and consistent running time improvements over the other known methods.The C++ implementations of the algorithms are available open-source as part of the LEMON graph and network optimization library.

In Silico Identification of Novel Orthosteric Inhibitors of Sphingosine Kinase 1 (SK1)

Sphingosine kinase 1 (SK1) overexpression and elevated sphingosine-1-phosphate (S1P) levels have been correlated with many disease states from cancer to inflammatory diseases to diabetes. Even though SK1 inhibitors are of consideberable interest as effective chemotherapeutic agents, poor potency, lack of selectivity and poor pharmacokinetic properties have been major problems in the first generation SK1 inhibitors. There is an urgent need for the discovery of novel in vivo, stable selective SK1 inhibitors with improved potency. The primary object of this study was to identify potential novel leads for orthosteric inhibition of SK1. We propose a series of compounds from different chemotypes as potential selective SK1 inhibitors via virtual screening of the ZINC database using ligand-based and structure-based pharmacophore models, molecular docking, substructure search, selectivity calculations. Molecular dynamics (MD) simulations revealed key insights into the binding mode and the stability of the SK1-ligand complex. Ten ligands were proposed as potential SK1 inhibitors based on the high induced fit docking scores, BEI, LLE and %HOA. Ligands 2, 3, 5 and 9 were found to be selective toward SK1 with favorable binding free energy of - 95 ± 5 kcal/mol. MD simulation of ligand 5 showed that the ligand-SK1 complex reached equilibrium with favorable hydrogen bonding and hydrophobic interactions. The four selective compounds have less than 0.24 similarity with previously discovered potent inhibitors. The proposed compounds may serve as potential novel leads for orthosteric inhibition of SK1.

The Next Generation Virgo Cluster Survey (NGVS). XXXII. A Search for Globular Cluster Substructures in the Virgo Galaxy Cluster Core

Abstract Substructure in globular cluster (GC) populations around large galaxies is expected in galaxy formation scenarios that involve accretion or merger events, and it has been searched for using direct associations between GCs and structure in the diffuse galaxy light, or with GC kinematics. Here, we present a search for candidate substructures in the GC population around the Virgo cD galaxy M87 through the analysis of the spatial distribution of the GC colors. The study is based on a sample of ∼1800 bright GCs with high-quality u, g, r, i, z, K s photometry, selected to ensure a low contamination by foreground stars or background galaxies. The spectral energy distributions of the GCs are associated with formal estimates of age and metallicity, which are representative of its position in a 4D color space relative to standard single stellar population models. Dividing the sample into broad bins based on the relative formal ages, we observe inhomogeneities that reveal signatures of GC substructures. The most significant of these is a spatial overdensity of GCs with relatively young age labels, of diameter ∼0.°1 (∼30 kpc), located to the south of M87. The significance of this detection is larger than about 5σ after accounting for estimates of random and systematic errors. Surprisingly, no large Virgo galaxy is present in this area that could potentially host these GCs. But candidate substructures in the M87 halo with equally elusive hosts have been described based on kinematic studies in the past. The number of GC spectra available around M87 is currently insufficient to clarify the nature of the new candidate substructure.

PBSM: An Efficient Top-K Subgraph Matching Algorithm

Top-K subgraph matching is one of the hot research issues in graph data management, which is to find, from the data graph, K subgraphs isomorphic to the query graph with the largest sum of weights. The existing methods of Top-K subgraph matching on large graphs usually use the filter-and-verify strategy. However, they all suffer from inefficiency in both stages. In the filtering stage, there exists repeated enumeration of vertices and the excessive memory cost of the filtering. In the verification stage, there exists redundant verification. Regarding to the above problems, we propose to use the preprocessing of the graph compression based on equivalent vertices to reduce the enumeration. In the filtering stage, we propose to reduce the memory cost by only considering the direct neighbors. In the verification stage, we take the vertex with the minimum number of candidate vertices in the query graph as the start vertex of the matching order, and use the idea of Ranking While Matching (RWM) to terminate the execution of the algorithm as early as possible by estimating the upper bound of the weights, so as to reduce redundant verification and improve the overall performance. Finally, the experimental results show that our method is much more efficient than existing methods in compression and the processing time.

Infalling groups and galaxy transformations in the cluster A2142

Context. Superclusters of galaxies provide dynamical environments for the study of the formation and evolution of structures in the cosmic web from galaxies, to the richest galaxy clusters, and superclusters themselves. Aims. We study galaxy populations and search for possible merging substructures in the rich galaxy cluster A2142 in the collapsing core of the supercluster SCl A2142, which may give rise to radio and X-ray structures in the cluster, and affect galaxy properties of this cluster. Methods. We used normal mixture modelling to select substructure of the cluster A2142. We compared alignments of the cluster, its brightest galaxies (hereafter BCGs), subclusters, and supercluster axes. The projected phase space (PPS) diagram and clustercentric distributions are used to analyse the dynamics of the cluster and study the distribution of various galaxy populations in the cluster and subclusters. Results. We find several infalling galaxy groups and subclusters. The cluster, supercluster, BCGs, and one infalling subcluster are all aligned. Their orientation is correlated with the alignment of the radio and X-ray haloes of the cluster. Galaxy populations in the main cluster and in the outskirts subclusters are different. Galaxies in the centre of the main cluster at the clustercentric distances 0.5 h−1 Mpc (Dc∕Rvir < 0.5, Rvir = 0.9 h−1 Mpc) have older stellar populations (with the median age of 10−11 Gyr) than galaxies at larger clustercentric distances. Star-forming and recently quenched galaxies are located mostly at the clustercentric distances Dc ≈ 1.8 h−1 Mpc, where subclusters fall into the cluster and the properties of galaxies change rapidly. In this region the median age of stellar populations of galaxies is about 2 Gyr. Galaxies in A2142 on average have higher stellar masses, lower star formation rates, and redder colours than galaxies in rich groups. The total mass in infalling groups and subclusters is M ≈ 6 × 1014 h−1 M⊙, that is approximately half of the mass of the cluster. This mass is sufficient for the mass growth of the cluster from redshift z = 0.5 (half-mass epoch) to the present. Conclusions. Our analysis suggests that the cluster A2142 has formed as a result of past and present mergers and infallen groups, predominantly along the supercluster axis. Mergers cause complex radio and X-ray structure of the cluster and affect the properties of galaxies in the cluster, especially at the boundaries of the cluster in the infall region. Explaining the differences between galaxy populations, mass, and richness of A2142, and other groups and clusters may lead to better insight about the formation and evolution of rich galaxy clusters.

Multilabel Remote Sensing Image Retrieval Using a Semisupervised Graph-Theoretic Method

Conventional supervised content-based remote sensing (RS) image retrieval systems require a large number of already annotated images to train a classifier for obtaining high retrieval accuracy. Most systems assume that each training image is annotated by a single label associated to the most significant semantic content of the image. However, this assumption does not fit well with the complexity of RS images, where an image might have multiple land-cover classes (i.e., multilabels). Moreover, annotating images with multilabels is costly and time consuming. To address these issues, in this paper, we introduce a semisupervised graph-theoretic method in the framework of multilabel RS image retrieval problems. The proposed method is based on four main steps. The first step segments each image in the archive and extracts the features of each region. The second step constructs an image neighborhood graph and uses a correlated label propagation algorithm to automatically assign a set of labels to each image in the archive by exploiting only a small number of training images annotated with multilabels. The third step associates class labels with image regions by a novel region labeling strategy, whereas the final step retrieves the images similar to a given query image by a subgraph matching strategy. Experiments carried out on an archive of aerial images show the effectiveness of the proposed method when compared with the state-of-the-art RS content-based image retrieval methods.

Exploiting graph kernels for high performance biomedical relation extraction

BackgroundRelation extraction from biomedical publications is an important task in the area of semantic mining of text. Kernel methods for supervised relation extraction are often preferred over manual feature engineering methods, when classifying highly ordered structures such as trees and graphs obtained from syntactic parsing of a sentence. Tree kernels such as the Subset Tree Kernel and Partial Tree Kernel have been shown to be effective for classifying constituency parse trees and basic dependency parse graphs of a sentence. Graph kernels such as the All Path Graph kernel (APG) and Approximate Subgraph Matching (ASM) kernel have been shown to be suitable for classifying general graphs with cycles, such as the enhanced dependency parse graph of a sentence.In this work, we present a high performance Chemical-Induced Disease (CID) relation extraction system. We present a comparative study of kernel methods for the CID task and also extend our study to the Protein-Protein Interaction (PPI) extraction task, an important biomedical relation extraction task. We discuss novel modifications to the ASM kernel to boost its performance and a method to apply graph kernels for extracting relations expressed in multiple sentences.ResultsOur system for CID relation extraction attains an F-score of 60%, without using external knowledge sources or task specific heuristic or rules. In comparison, the state of the art Chemical-Disease Relation Extraction system achieves an F-score of 56% using an ensemble of multiple machine learning methods, which is then boosted to 61% with a rule based system employing task specific post processing rules. For the CID task, graph kernels outperform tree kernels substantially, and the best performance is obtained with APG kernel that attains an F-score of 60%, followed by the ASM kernel at 57%. The performance difference between the ASM and APG kernels for CID sentence level relation extraction is not significant. In our evaluation of ASM for the PPI task, ASM performed better than APG kernel for the BioInfer dataset, in the Area Under Curve (AUC) measure (74% vs 69%). However, for all the other PPI datasets, namely AIMed, HPRD50, IEPA and LLL, ASM is substantially outperformed by the APG kernel in F-score and AUC measures.ConclusionsWe demonstrate a high performance Chemical Induced Disease relation extraction, without employing external knowledge sources or task specific heuristics. Our work shows that graph kernels are effective in extracting relations that are expressed in multiple sentences. We also show that the graph kernels, namely the ASM and APG kernels, substantially outperform the tree kernels. Among the graph kernels, we showed the ASM kernel as effective for biomedical relation extraction, with comparable performance to the APG kernel for datasets such as the CID-sentence level relation extraction and BioInfer in PPI. Overall, the APG kernel is shown to be significantly more accurate than the ASM kernel, achieving better performance on most datasets.

An extension of the Fries rule to non-benzenoid hydrocarbons having four-atomic rings

The study contains a deductive search for the principal monocyclic substructures determining different importances (weights) of separate Kekule valence structures of phenylenes and their congeners. Individual Kekule structures are modelled as continuous conjugated systems consisting of uniform double (C=C) bonds connected by uniform single (C–C) bonds, the latter being substantially weaker as compared to the former. The relevant total $$\pi$$ -electron energies are shown to offer an adequate criterion for ordering of the structures concerned according to their weights. These energies, in turn, are derived in the form of power series with respect to the small resonance parameter of C–C bonds. Analysis of expressions for separate members of this series shows that the cyclobutadienoid rings (if any) are the most important destabilizing contributors to the energy of the given structure, whereas the benzenoid rings and cycles like 3,4-dimethylene cyclobutene take the second place (their increments are stabilizing and destabilizing, respectively). Additivity and transferability of the above-enumerated contributions to energies of Kekule valence structures also are among the conclusions. These results provide us with an extension of the classical Fries rule to non-benzenoid hydrocarbons having four-atomic rings. Specific examples of the given class of compounds are considered in a detail, viz. biphenylene, [3]phenylene, as well as benzo- and naphthocyclobutenes. The relation of the approach applied to the theory of conjugated circuits also is discussed.

Redesign of the gStore system

gStore is an open-source native Resource Description Framework (RDF) triple store that answers SPARQL queries by subgraph matching over RDF graphs. However, there are some deficiencies in the original system design, such as answering simple queries (including onetriple pattern queries). To improve the efficiency of the system, we reconsider the system design in this paper. Specifically, we propose a new query plan generation module that generates different query plans according to the structures of query graphs. Furthermore, we re-design our vertex encoding strategy to achieve more pruning power and a new multi-join algorithm to speed up the subgraph matching process. Extensive experiments on synthetic and real RDF datasets show that our method outperforms the state-of-the-art algorithms significantly.

The sufficiency of the divisibility condition for 20 divides K(m, n, s)

F. Harary, R.W. Robinson and N.C. Wormald studied a complete tripartite graph K(m, n, s), and putted forward the conjecture, for t|(mn + ms + ns), t > 1 and t is even, then G has a t isomorphic factorization subgraphs. For t divides mn + ms + ns and t = 2, 4, they obtained that then G has a t isomorphic factorization subgraphs. In this paper, we used the decomposition and Congruential method and obtained the conjecture is true for t = 20.

Location Aware and Node Ranking Value-Assisted Embedding Algorithm for One-Stage Embedding in Multiple Distributed Virtual Network Embedding

Network virtualization (NV) is one crucial attribute for the next-generation network. Virtual network embedding (VNE) is known to be the resource allocation problem in NV content. Since 2008, researchers have proposed multiple embedding algorithms to embed VNs onto the underlying physical networks. Considering the NP-hard nature of VNE, most of the prior algorithms focus on embedding each VN in two separated embedding stages (separated node and link embeddings). Some embedding algorithms embed each VN in one embedding stage by adopting a mixed integer linear programming approach or game theory or sub-graph isomorphism, trapped in high computation time. These algorithms embed the VN in one centralized substrate network (SN), while, in real networking environment, each VN must be embedded among multiple SNs. Each substrate node is geographically distributed in a different location. In order to address these issues, we propose a Location-Aware and Node Ranking Value Assisted embedding algorithm (labeled as LANRVA-VNE). The LANRVA-VNE conducts each VN embedding in one embedding stage. In addition, the LANRVA-VNE is able to embed each requested VN service among multiple distributed SNs in polynomial time, aiming at promoting future dynamic VN service implementation. Main evaluation results reveal that the LANRVA-VNE significantly improves VN acceptance ratio by at least 10% over the typical two-stage algorithms (e.g., VNE-NTANRC-S, RW-SP, and ViNE-SP).

A Comparative Study of Subgraph Matching Isomorphic Methods in Social Networks

With the fast development of social networks, more and more data has been generated. Finding useful information among these data is important. Subgraph matching is the method that can be used in social networks for social search, recommender systems, and so on. In this paper, we choose five typical graph matching methods which are VF2, SPath, TurboISO, BoostIso, and RI to value their performance and scalability in social networks. These methods are verified by three social network data sets whose node’s number vary from thousands to millions. According to the experiments, we can find that VF2 and RI is applicable for rather small graphs while SPath performs better in large graph when average degree of graph is small. When graph with high average degree, TurboISO and BoostIso performs better. What is more, we also compare the efficiency of different matching order when searching. The order choosing strategy proposed by RI is better.

Crossing Scientific Workflow Fragments Discovery Through Activity Abstraction in Smart Campus

Considering the knowledge-intensity and error-prone of developing scientific workflows from scratch, reusing and repurposing current workflows are the effective and efficient solution to support scientists for conducting novel experiments, and this strategy is deemed as important to achieve the objective of smart campus. An experiment may be relevant with one or multiple scientific workflows. This observation drives us to propose a technique that can discover and recommend cross-workflow fragments with respect to the requirement of novel experiments. Specifically, the functionally similar activities are clustered through adopting a modularity-based community discovery clustering technique, and they are represented as abstract activities. An abstract activity network model is constructed accordingly to reflect the invocation relations among abstract activities. Structural and semantic similar workflow fragments are discovered from the abstract activity network through the sub-graph matching algorithm. These fragments are instantiated through replacing abstract activities by appropriate activities in certain activity clusters. These instantiated workflow fragments are ranked and recommended for their reuse and repurposing purpose. Experimental evaluation results demonstrate that our technique is accurate and efficient on discovering and recommending appropriate cross-workflow fragments.

A New Framework of Frequent Uncertain Subgraph Mining

Nowadays, frequent graph mining approaches are very popular in several applications and big data domains. However, some problems are still not solved and need more attention from researchers such as inexact subgraph matching when similarity among subgraphs is not totally proved. Furthermore, many research works dealt with structural graph matching, but a little attention was paid to semantic graph matching when graph vertices and/or edges are attributed and typed. Therefore, this paper proposes a new possibilistic flexible graph mining approach to discover similar subgraphs, by applying possibilistic similarity rather than using hard structural exact similarity. This novel approach is hybrid and uses two similarity measures. An approximate structural similarity function of graph edit distance function and a semantic vertices similarity function based on possibilistic information affinity function. Experimental evaluation was conducted on real datasets borrowed from various domains and tests have shown a highly superiority of our hybrid frequent subgraph mining approach by achieving a good time processing performance and simultaneously discovering more similar subgraphs.