Subgraph Isomorphism Research Articles

Subgraph Matching With Effective Matching Order and Indexing

Subgraph matching finds all embeddings from a data graph that are identical to a query graph. Recent algorithms work by generating a tree-structured index on the data graph based on the query graph, ordering the vertices path-by-path in the tree, and enumerating the embeddings following the matching order. However, we find such path-based ordering and tree-structured index based enumeration inherently limit the performance due to the lack of consideration on the edges among the vertices across tree paths. To address this problem, we propose an approach that generates the matching order based on a cost model considering both the edges among query vertices and the number of candidates. Furthermore, we create a bigraph index for candidate vertices and their selected neighbors in the data graph, and use this index to perform enumeration along the matching order. Our experiments on both real-world and synthetic datasets show that our method outperforms the state of the art by orders of magnitude.

NSDroid: efficient multi-classification of android malware using neighborhood signature in local function call graphs

With the rapid development of mobile Internet, Android applications are used more and more in people’s daily life. While bringing convenience and making people’s life smarter, Android applications also face much serious security and privacy issues, e.g., information leakage and monetary loss caused by malware. Detection and classification of malware have thus attracted much research attention in recent years. Most current malware detection and classification approaches are based on graph-based similarity analysis (e.g., subgraph isomorphism), which is well known to be time-consuming, especially for large graphs. In this paper, we propose NSDroid, a time-efficient malware multi-classification approach based on neighborhood signature in local function call graphs (FCGs). NSDroid uses a approach based on neighborhood signature to calculate the similarity of different applications’ FCGs, which is significantly faster than traditional approaches based on subgraph isomorphism. For each node in the FCGs, NSDroid uses a fixed-length neighborhood signature to capture the caller-callee relationship between different functions and combines neighborhood signatures of all nodes to form a vector that characterizes the function call relationship in the whole application. The generated signature vector is fed into a SVM-based classifier to determine which family the malware belongs to. Experimental results on large-scale benchmarks show that, compared with state-of-the-art solutions, NSDroid reduces average detection latency by nearly $$20\times $$ , and meanwhile improves many evaluation index such as recall rate and others.

Dynamical Relics of the Ancient Galactic Halo

Abstract We search for dynamical substructures in the LAMOST DR3 very metal-poor (VMP) star catalog. After cross-matching with Gaia DR2, there are ∼3300 VMP stars with available high-quality astrometric information that have halo-like kinematics. We apply a method based on the self-organizing map StarGO to find groups clustered in the 4D space of orbital energy and angular momentum. We identify 57 dynamically tagged groups (DTGs), which we label DTG-1 to DTG-57. Most of them belong to existing massive substructures in the nearby halo, such as the Gaia Sausage or Sequoia. The stream identified by Helmi et al. is recovered, but the two disjointed portions of the substructure appear to have distinct dynamical properties. The very retrograde substructure Rg5 found previously by Myeong et al. is also retrieved. We report six new DTGs with highly retrograde orbits, two with very prograde orbits, and 12 with polar orbits. By mapping other data sets (APOGEE halo stars, and catalogs of r-process-enhanced and carbon-enhanced metal-poor [CEMP] stars) onto the trained neuron map, we can associate stars with detailed chemical abundances with the DTGs and look for associations with chemically peculiar stars. The highly eccentric Gaia Sausage groups contain representatives of both debris from the satellite itself (which is α-poor) and the Splashed Disk, sent up into eccentric halo orbits from the encounter (and which is α-rich). The new prograde substructures also appear to be associated with the Splashed Disk. The DTGs belonging to the Gaia Sausage host two relatively metal-rich r-II stars and six CEMP stars in different subclasses, consistent with the idea that the Gaia Sausage progenitor is a massive dwarf galaxy. Rg5 is dynamically associated with two highly r-process-enhanced stars with [Fe/H] ∼ −3. This finding indicates that its progenitor might be an ultrafaint dwarf galaxy that has experienced r-process enrichment from neutron star mergers.

DAMBA: Detecting Android Malware by ORGB Analysis

With the rapid development of smart devices, mobile phones have permeated many aspects of our life. Unfortunately, their widespread popularization attracted endless attacks that are serious threats for users. As the mobile system with the largest market share, Android has already become the hardest hit for years. To Detect Android Malware by ORGB Anlysis, in this paper, we present DAMBA, a novel prototype system based on a C/S architecture. DAMBA extracts the static and dynamic features of apps. For further analyses, we propose TANMAD algorithm, a two-step Android malware detection algorithm, which reduces the range of possible malware families, and then utilizes subgraph isomorphism matching for malware detection. The key novelty of this paper is the modeling of object reference information by constructing directed graphs, which is called object reference graph birthmarks (ORGB). To achieve better efficiency and accuracy, in this paper, we present several optimization strategies for hybrid analysis. DAMBA is evaluated on a large real-world dataset of 2239 malicious and 1000 popular benign apps. The detection accuracy reaches 100% in most cases, and the average detection time is less than 5 s. Experimental results show that DAMBA outperforms the well-known detector, McAfee, which is based on signature recognition. In addition, DAMBA is demonstrated to resist the known malware attacks and their variants efficiently, as well as malware that uses obfuscation techniques.

NeuroPath2Path: Classification and elastic morphing between neuronal arbors using path-wise similarity.

Neuron shape and connectivity affect function. Modern imaging methods have proven successful at extracting morphological information. One potential path to achieve analysis of this morphology is through graph theory. Encoding by graphs enables the use of high throughput informatic methods to extract and infer brain function. However, the application of graph-theoretic methods to neuronal morphology comes with certain challenges in term of complex subgraph matching and the difficulty in computing intermediate shapes in between two imaged temporal samples. Here we report a novel, efficacious graph-theoretic method that rises to the challenges. The morphology of a neuron, which consists of its overall size, global shape, local branch patterns, and cell-specific biophysical properties, can vary significantly with the cell's identity, location, as well as developmental and physiological state. Various algorithms have been developed to customize shape based statistical and graph related features for quantitative analysis of neuromorphology, followed by the classification of neuron cell types using the features. Unlike the classical feature extraction based methods from imaged or 3D reconstructed neurons, we propose a model based on the rooted path decomposition from the soma to the dendrites of a neuron and extract morphological features from each constituent path. We hypothesize that measuring the distance between two neurons can be realized by minimizing the cost of continuously morphing the set of all rooted paths of one neuron to another. To validate this claim, we first establish the correspondence of paths between two neurons using a modified Munkres algorithm. Next, an elastic deformation framework that employs the square root velocity function is established to perform the continuous morphing, which, as an added benefit, provides an effective visualization tool. We experimentally show the efficacy of NeuroPath2Path, NeuroP2P, over the state of the art.

Top-[formula omitted] user-specified preferred answers in massive graph databases

There are numerous applications where users wish to identify subsets of vertices in a social network or graph database that are of interest to them. They may specify sets of patterns and vertex properties, and each of these confers a score to a subgraph. The users want to find the subgraphs with top-k highest scores. Examples in the real world where such subgraphs involve custom scoring methods include: techniques to identify sets of coordinated influence bots on Twitter, methods to identify suspicious subgraphs of nodes involved in nuclear proliferation networks, and sets of sockpuppet accounts seeking to illicitly influence star ratings on e-commerce platforms. All of these types of applications have numerous custom scoring methods. This motivates the concept of Scoring Queries presented in this paper — unlike past work, an important aspect of scoring queries is that the users get to choose the scoring mechanism, not the system. We present the Advanced top-k (ATK) algorithm and show that it intelligently leverages graph indexes from the past but also presents novel pruning opportunities. We present an implementation of ATK showing that it beats out a baseline algorithm that builds on advanced subgraph matching methods with multiple graph database backends including Jena and GraphDB. We show that ATK scales well on real world graph databases from YouTube, Flickr, IMDb, and CiteSeerX.

부분 그래프 동형 문제를 위한 동적 매칭 순서들의 성능 비교

최근 다양한 분야에서 NP-hard에 속하는 그래프 문제를 효율적으로 해결하는 것이 점차 중요해지고 있다. 그래프 분석에서 가장 핵심적인 문제 중 하나는 부분 그래프 동형(subgraph isomorphism)문제이다. 부분 그래프 동형 문제란 데이터 그래프와 쿼리 그래프가 주어졌을 때, 데이터 그래프에서 쿼리그래프의 모든 임베딩(embedding)을 찾는 문제이다. 이 문제를 해결하는 최신 알고리즘인 DAF에서는 후보 수 순서(candidate-size order)와 경로 수 순서(path-size order)라는 두 가지 동적 매칭 순서를 제시하였다. 하지만 구체적으로 어떤 경우에 두 가지 동적 매칭 순서의 성능 차이가 일어나는지는 언급되지 않았다. 본 논문에서는 다양한 그래프에서 두 가지 동적 매칭 순서의 성능을 비교하여 쿼리 그래프의 트리 형태 경로(tree-like path)의 평균 길이가 길어지거나 데이터 그래프의 레이블(label) 개수가 줄어들수록 경로 수 순서의 효율성이 높아지는 것을 밝혔다.

Super-resolution fluorescence-assisted diffraction computational tomography reveals the three-dimensional landscape of the cellular organelle interactome

The emergence of super-resolution (SR) fluorescence microscopy has rejuvenated the search for new cellular sub-structures. However, SR fluorescence microscopy achieves high contrast at the expense of a holistic view of the interacting partners and surrounding environment. Thus, we developed SR fluorescence-assisted diffraction computational tomography (SR-FACT), which combines label-free three-dimensional optical diffraction tomography (ODT) with two-dimensional fluorescence Hessian structured illumination microscopy. The ODT module is capable of resolving the mitochondria, lipid droplets, the nuclear membrane, chromosomes, the tubular endoplasmic reticulum, and lysosomes. Using dual-mode correlated live-cell imaging for a prolonged period of time, we observed novel subcellular structures named dark-vacuole bodies, the majority of which originate from densely populated perinuclear regions, and intensively interact with organelles such as the mitochondria and the nuclear membrane before ultimately collapsing into the plasma membrane. This work demonstrates the unique capabilities of SR-FACT, which suggests its wide applicability in cell biology in general.

An invariant descriptor map for 3D objects matching

Meshes and point clouds are traditionally used to represent and match 3D shapes. The matching prob-lem can be formulated as finding the best one-to-one correspondence between featured regions of two shapes. This paper presents an efficient and robust 3D matching method using vertices descriptors de-tection to define feature regions and an optimization approach for regions matching. To do so, we compute an invariant shape descriptor map based on 3D surface patches calculated using Zernike coef-ficients. Then, we propose a multi-scale descriptor map to improve the measured descriptor map quali-ty and to deal with noise. In addition, we introduce a linear algorithm for feature regions segmentation according to the descriptor map. Finally, the matching problem is modelled as sub-graph isomorphism problem, which is a combinatorial optimization problem to match feature regions while preserving the geometric. Finally, we show the robustness and stability of our method through many experimental re-sults with respect to scaling, noise, rotation, and translation. Â

Optimized Distributed Subgraph Matching Algorithm Based on Partition Replication

At present, with the explosive growth of data scale, subgraph matching for massive graph data is difficult to satisfy with efficiency. Meanwhile, the graph index used in existing subgraph matching algorithm is difficult to update and maintain when facing dynamic graphs. We propose a distributed subgraph matching algorithm based on Partition Replica (noted as PR-Match) to process the partition and storage of large-scale data graphs. The PR-Match algorithm first splits the query graph into sub-queries, then assigns the sub-query to each node for sub-graph matching, and finally merges the matching results. In the PR-Match algorithm, we propose a heuristic rule based on prediction cost to select the optimal merging plan, which greatly reduces the cost of merging. In order to accelerate the matching speed of the sub-query graph, a vertex code based on the vertex neighbor label signature is proposed, which greatly reduces the search space for the subquery. As the vertex code is based on the increment, the problem that the feature-based graph index is difficult to maintain in the face of the dynamic graph is solved. An abundance of experiments on real and synthetic datasets demonstrate the high efficiency and strong scalability of the PR-Match algorithm when handling large-scale data graphs.

Partial Matching of Large Scale Process Plant Models Using Random Walk on Graphs

3D process plant models(PPMs) in the process industry normally consists of thousands of components. And, there are many similar local structures in the PPM. Due to the complex process flow, the topology relationship among components is very complicated. Therefore, designing a new PPM is quite time consuming. In order to shorten the design cycle, content based model retrieval for PPMs is an imperative requirement. In this paper, we propose a partial matching framework for PPMs based on graph matching aiming at improving design efficiency and realizing design reuse. The random walk algorithm is employed to distinguish similar local structures. Specifically, each PPM is represented by an undirected labeled graph. The local topological feature of each component is extracted based on the random walk algorithm. For partial matching, a subgraph isomorphism algorithm is introduced. The matching process is accelerated by using the local topological feature to generate an optimized initial state and alleviate the computation of feasible rules. Experimental results show the feasibility and effectiveness of our matching framework.

An efficient mining algorithm for maximal frequent patterns in uncertain graph database

Mining maximal frequent patterns is significant in many fields, but the mining efficiency is often low. The bottleneck lies in too many candidate subgraphs and extensive subgraph isomorphism tests. In this paper we propose an efficient mining algorithm. There are two key ideas behind the proposed methods. The first is to divide each edge of every certain graph (converted from equivalent uncertain graph) and build search tree, avoiding too many candidate subgraphs. The second is to search the tree built in the first step in order, avoiding extensive subgraph isomorphism tests. The evaluation of our approach demonstrates the significant cost savings with respect to the state-of-the-art approach not only on the real-world datasets as well as on synthetic uncertain graph databases.

Filtered prioritized and cluster-based optimization towards correction of antipatterns

When systems evolve, the maintainability and the complexity of the system increase, resulting in the poor antidesign patterns or antipatterns in software maintenance. Refactoring is an operation used to improve the structure of an existing system by changing its internal structure without affecting its external behavior. Many studies revealed that refactoring is underused by software development team in industry due to its increased effort and lack of knowledge about existing approaches. Thus, a prioritized correction of antipatterns based on relevance of classes, analyzed development history, risk to refactor, minimized code changes, and maintainers context and preferences is needed for good refactoring recommendations. We propose an approach based on filtered relevant classes with generic linkage-based clustering and adapted nondominated sorting genetic algorithm III to find good refactoring recommendations, which maximize the software quality and reduce the refactoring effort. Our approach uses our own node centrality-based sub-graph isomorphism algorithm to dynamically understand the system with good accuracy prior to optimization. Our approach is evaluated on six open-source systems and the results have shown the effectiveness of our approach compared to the other existing ones.

An Efficient Framework for Multiple Subgraph Pattern Matching Models

With the popularity of storing large data graph in cloud, the emergence of subgraph pattern matching on a remote cloud has been inspired. Typically, subgraph pattern matching is defined in terms of subgraph isomorphism, which is an NP-complete problem and sometimes too strict to find useful matches in certain applications. And how to protect the privacy of data graphs in subgraph pattern matching without undermining matching results is an important concern. Thus, we propose a novel framework to achieve the privacy-preserving subgraph pattern matching in cloud. In order to protect the structural privacy in data graphs, we firstly develop a k-automorphism model based method. Additionally, we use a cost-model based label generalization method to protect label privacy in both data graphs and pattern graphs. During the generation of the k-automorphic graph, a large number of noise edges or vertices might be introduced to the original data graph. Thus, we use the outsourced graph, which is only a subset of a k-automorphic graph, to answer the subgraph pattern matching. The efficiency of the pattern matching process can be greatly improved in this way. Extensive experiments on real-world datasets demonstrate the high efficiency of our framework.

Qubit allocation as a combination of subgraph isomorphism and token swapping

In 2016, the first quantum processors have been made available to the general public. The possibility of programming an actual quantum device has elicited much enthusiasm. Yet, such possibility also brought challenges. One challenge is the so called Qubit Allocation problem: the mapping of a virtual quantum circuit into an actual quantum architecture. There exist solutions to this problem; however, in our opinion, they fail to capitalize on decades of improvements on graph theory. In contrast, this paper shows how to model qubit allocation as the combination of Subgraph Isomorphism and Token Swapping. This idea has been made possible by the publication of an approximative solution to the latter problem in 2016. We have compared our algorithm against five other qubit allocators, all independently designed in the last two years, including the winner of the IBM Challenge. When evaluated in "Tokyo", a quantum architecture with 20 qubits, our technique outperforms these state-of-the-art approaches in terms of the quality of the solutions that it finds and the amount of memory that it uses, while showing practical runtime.

A unifying view of explicit and implicit feature maps of graph kernels

Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. We investigate how convolution kernels for structured data are composed from base kernels and construct corresponding feature maps. On this basis we propose exact and approximative feature maps for widely used graph kernels based on the kernel trick. We analyze for which kernels and graph properties computation by explicit feature maps is feasible and actually more efficient. In particular, we derive approximative, explicit feature maps for state-of-the-art kernels supporting real-valued attributes including the GraphHopper and graph invariant kernels. In extensive experiments we show that our approaches often achieve a classification accuracy close to the exact methods based on the kernel trick, but require only a fraction of their running time. Moreover, we propose and analyze algorithms for computing random walk, shortest-path and subgraph matching kernels by explicit and implicit feature maps. Our theoretical results are confirmed experimentally by observing a phase transition when comparing running time with respect to label diversity, walk lengths and subgraph size, respectively.

The Application Study of Subgraph Isomorphism in the SDMA

To meet the need for low delay of end-to-end data transmission in some particular application of mobile ad hoc network (MANET), the planning SDMA slot tables are usually adopted. Whether the message can be transmitted by the planning SDMA slot table must be judged to decide if the pattern topology graph according to the SDMA slot table is included in the target topology graph, which was solved by employing subgraph isomorphism model in this paper, and a new algorithm named SGI (subgraph isomorphism) was proposed based on the Ullmann’s. Simulation and analysis showed that compared with Ullmann’s, the SGI could judge the subgraph isomorphism relationship more quickly with lower computing overhead.

A new framework for subimage analysis

We develop new methods for several subimage analysis problems. Images in two dimensions are represented by matrixes (higher dimensional images are represented by higher dimensional arrays). This representation yields efficient algorithms for image search and comparison problems applicable not only to images, but also to array search and comparison in any dimension two or larger. Subimage analysis based on our array-representation has limitations. For example, our methods are not rotation and scale invariant. However, they yield efficient algorithms that have practical applications. Videos and snapshots taken from videos are continuously added to the digital world where they are permanently accessible. From a snapshot, one may want to locate and watch the part of the video that contains this snapshot (e.g. moments in news-footage, soccer or olympic games). One may also want to find common parts (sequences of frames) in multiple videos for various reasons (e.g. copyright-check, false-news detection). Our algorithms are applicable in these cases. For another application, we propose representing RNA secondary structures by matrixes. Since our methods are applicable to submatrix analysis, RNA substructure search and multiple RNA structure comparison problems can be solved by using our algorithms (for exact matches).

Graph pattern matching with counting quantifiers and label-repetition constraints

In recent years, we have witnessed an increasing use of graph pattern matching in a wide variety of applications such as social networks analysis, knowledge discovery, software plagiarism detection and many more. It is typically defined in terms of subgraph isomorphism, an NP-Complete problem. To overcome this cost, many extensions of graph simulation have been proposed that allow graph pattern matching to be conducted in cubic-time. However, in emerging applications, more expressive patterns are needed, notably ones with counting quantifiers (CQs) which are not considered by simulation-based approaches. In this article, we propose a simulation-based graph pattern matching approach that supports CQs on edges of graph patterns. We first consider CQs that express numeric aggregates only. We show that our approach is in ptime as earlier extensions of graph simulation by providing a cubic-time quantified matching algorithm, i.e., an algorithm for matching graph patterns that contain CQs. In the second part, we discuss the problem of Label-Repetition Constraints (LRCs). We define a necessary and sufficient condition for the satisfaction of LRCs. Based on this condition, we give an extension of our quantified matching algorithm to deal with LRCs in ptime, together with an optimization technique. Finally, we show that our quantified graph pattern matching approach retains the same complexity bounds when dealing with ratio aggregates. To our knowledge, this is the first effort to deal with numeric aggregates, ratio aggregates, and LRCs on graph patterns in ptime.

Identification via a Parallel Hit Progression Strategy of Improved Small Molecule Inhibitors of the Malaria Purine Uptake Transporter that Inhibit Plasmodium falciparum Parasite Proliferation.

Emerging resistance to current antimalarial medicines underscores the importance of identifying new drug targets and novel compounds. Malaria parasites are purine auxotrophic and import purines via the Plasmodium falciparum equilibrative nucleoside transporter type 1 (PfENT1). We previously showed that PfENT1 inhibitors block parasite proliferation in culture. Our goal was to identify additional, possibly more optimal chemical starting points for a drug discovery campaign. We performed a high throughput screen (HTS) of GlaxoSmithKline's 1.8 million compound library with a yeast-based assay to identify PfENT1 inhibitors. We used a parallel progression strategy for hit validation and expansion, with an emphasis on chemical properties in addition to potency. In one arm, the most active hits were tested for human cell toxicity; 201 had minimal toxicity. The second arm, hit expansion, used a scaffold-based substructure search with the HTS hits as templates to identify over 2000 compounds; 123 compounds had activity. Of these 324 compounds, 175 compounds inhibited proliferation of P. falciparum parasite strain 3D7 with IC50 values between 0.8 and ∼180 μM. One hundred forty-two compounds inhibited PfENT1 knockout (pfent1Δ) parasite growth, indicating they also hit secondary targets. Thirty-two hits inhibited growth of 3D7 but not pfent1Δ parasites. Thus, PfENT1 inhibition was sufficient to block parasite proliferation. Therefore, PfENT1 may be a viable target for antimalarial drug development. Six compounds with novel chemical scaffolds were extensively characterized in yeast-, parasite-, and human-erythrocyte-based assays. The inhibitors showed similar potencies against drug sensitive and resistant P. falciparum strains. They represent attractive starting points for development of novel antimalarial drugs.