Subgraph Isomorphism Research Articles

A novel subgraph querying method based on paths and spectra

Graph and graph database are widely used in many domains, and the graph querying attracts more and more attentions. Among these querying problems, subgraph querying is the most compelling one, since it contains very expensive subgraph isomorphism. The paper proposes a novel subgraph querying method PLGCoding, which use some information of shortest paths and Laplacian spectra to filter out false positives. Specifically, we first extract some features, including some information of vertices, edges, the shortest paths and Laplacian spectra, and encode extracted features. An index PLGCode-Tree is built based on codes to shrink the candidate set. Then, we propose two-step filtering strategy to implement the filtering-and-verification framework and thus generate the answer set. Compared with competing methods on real dataset, experimental results show PLGCoding can improve the querying efficiency.

SISE: Self-Updating of Indoor Semantic Floorplans for General Entities

Indoor semantic floorplan is important for a range of location based service (LBS) applications, attracting many research efforts in several years. In many cases, the out-of-date indoor semantic floorplans would gradually deteriorate and even break down the LBS performance. Thus, it is important to automatically update changed semantics of indoor floorplans caused by environmental variation. However, few research has been focused on the continuous semantic updating problem. This paper presents SISE as a mobile crowdsourcing system that uses a new abstraction for indoor general entities and their semantics, enGraph, to automatically update changed semantics of indoor floorplans using images and inertial data. We first propose efficient methods to generate enGraph. Thus, an image can be associated with an indoor semantic floorplan. Accordingly, we formulate the enGraph matching problem and then propose a quality-based maximum common subgraph matching algorithm so that entities extracted from an image can be corresponded to entities in the indoor semantic floorplan. Furthermore, we propose a quadrant comparison algorithm and a region shrink based localization algorithm to detect and localize changed entities. Thus, the new semantics can be labeled and out-of-date semantics can be removed. Extensive experiments have been conducted on real and synthetic data. Experimental results show that 80 percent of out-of-date semantics of indoor general entities can be updated by SISE.

A fast deterministic detection of small pattern graphs in graphs without large cliques

We show that for several pattern graphs on four vertices (e.g., C4), their induced copies in host graphs with n vertices and no clique on k+1 vertices can be deterministically detected in O(n2.5719k0.3176+n2k2) time for k<n0.394 and O(n2.5k0.5+n2k2) time for k≥n0.394. The aforementioned pattern graphs have a pair of non-adjacent vertices whose neighborhoods are equal. By considering dual graphs, in the same asymptotic time, we can also detect four vertex pattern graphs, that have an adjacent pair of vertices with the same neighbors among the remaining vertices (e.g., K4), in host graphs with n vertices and no independent set on k+1 vertices.By using the concept of Ramsey numbers, we can extend our method for induced subgraph isomorphism to include larger pattern graphs having a set of independent vertices with the same neighborhood and n-vertex host graphs without cliques on k+1 vertices (as well as the pattern graphs and host graphs dual to the aforementioned ones, respectively).

Glycosciences.DB: an annotated data collection linking glycomics and proteomics data (2018 update).

Glycosciences.DB, the glycan structure database of the Glycosciences.de portal, collects various kinds of data on glycan structures, including carbohydrate moieties from worldwide Protein Data Bank (wwPDB) structures. This way it forms a bridge between glycomics and proteomics resources. A major update of this database combines a redesigned web interface with a series of new functions. These include separate entry pages not only for glycan structures but also for literature references and wwPDB entries, improved substructure search options, a newly available keyword search covering all types of entries in one query, and new types of information that is added to glycan structures. These new features are described in detail in this article, and options how users can provide information to the database are discussed as well. Glycosciences.DB is available at http://www.glycosciences.de/database/ and can be freely accessed.

Plant Species Identification from Occluded Leaf Images

We present an approach to identify the plant species from the contour information from occluded leaf image using a database of full plant leaves. Although contour based 2D shape matching has been studied extensively in the last couple of decades, matching occluded leaves with full leaf databases is an open and little worked on problem. Classifying occluded plant leaves is even more challenging than full leaf matching because of large variations and complexity of leaf structures. Matching an occluded contour with all the full contours in a database is an NP-hard problem, so our algorithm is necessarily suboptimal. First, we represent the 2D contour points as a β-Spline curve. Then, we extract interest points on these curves via the Discrete Contour Evolution (DCE) algorithm. We use subgraph matching using the DCE points as graph nodes, which produces a number of open curves for each closed leaf contour. Next, we compute the similarity transformation parameters (translation, rotation, and uniform scaling) for each open curve. We then "overlay" each open curve with the inverse similarity transformed occluded curve and use the Fréchet distance metric to measure the quality of the match, retaining the best η matched curves. Since the Fréchet metric is cheap to compute but not perfectly correlated with the quality of the match, we formulate an energy functional that is well correlated with the quality of the match, but is considerably more expensive to compute. The functional uses local and global curvature, Shape Context descriptors, and String Cut features. We minimize this energy functional using a convex-concave relaxation framework. The curve among these best η curves, that has the minimum energy, is considered to be the best overall match with the occluded leaf. Experiments on three publicly available leaf image database shows that our method is both effective and efficient, outperforming other current state-of-the-art methods. Occlusion is measured as the percentage of the overall contour (and not leaf area) that is missing. We show that our algorithm can, even for leaves with a high amounts of occlusion (say 50 percent occlusion), still identify the best full leaf match from the databases.

On Minimal Unique Induced Subgraph Queries

In this paper, a novel type of interesting subgraph query is proposed: Minimal Unique Induced Subgraph (MUIS) query. Given a (large) graph G and a query vertex (position) q in the graph, can we find an induced subgraph containing q with the minimal number of vertices that is unique in G? MUIS query has many potential applications, such as subgraph retrieval, graph visualization, representative subgraph discovery and vertex property exploration. The formal definition of MUIS is given and the properties are discussed in this paper. The baseline and EQA (Efficient Query Answering) algorithms are proposed to solve the MUIS query problem under the filtering-validation framework. In the EQA algorithm, the Breadth First Search (BFS)-based candidate set generation strategy is proposed to ensure the minimality property of MUIS; the matched vertices-based pruning strategy is proposed to prune useless candidate sets and the unnecessary subgraph isomorphism; and the query position-based subgraph isomorphism is proposed to check efficiently the uniqueness of the subgraphs. Experiments are carried on real datasets and synthetic datasets to verify the effectiveness and efficiency of the proposed algorithm under novel measurements. The influencing factors of the process speed are discussed at last in the paper.

TBSGM

Subgraph matching, which belongs to NP-hard, faces significant challenges on a large scale graph with billions of nodes, and existing methods are usually confronted with greater challenges from both stability and efficiency. In this article, a subgraph matching method in a distributed system, tree model-based subgraph matching method (TBSGM) is proposed. The authors provide a transformed efficient query tree as a replacement for a query graph. In order to get the tree, they present a cost evaluation model which may help to generate the efficient query tree according to network communication-cost and calculation-cost evaluation. Also, a key set based indexing strategy for intermediate results is given to simplify the matching results during network communication. Extensive experiments with real-world datasets show that TBSGM significantly outperforms other methods in the aspects of scalability and efficiency.

Using partial evaluation in holistic subgraph search

Because of its wide application, the subgraph matching problem has been studied extensively during the past decade. However, most existing solutions assume that a data graph is a vertex/edge-labeled graph (i.e., each vertex/edge has a simple label). These solutions build structural indices by considering the vertex labels. However, some real graphs contain rich-content vertices such as user profiles in social networks and HTML pages on the World Wide Web. In this study, we consider the problem of subgraph matching using a more general scenario. We build a structural index that does not depend on any vertex content. Based on the index, we design a holistic subgraph matching algorithm that considers the query graph as a whole and finds one match at a time. In order to further improve efficiency, we propose a “partial evaluation and assembly” framework to find subgraph matches over large graphs. Last but not least, our index has light maintenance overhead. Therefore, our method can work well on dynamic graphs. Extensive experiments on real graphs show that our method outperforms the state-of-the-art algorithms.

Edge orbits and cyclic and [formula omitted]-pyramidal decompositions of complete uniform hypergraphs

Let Zn denote the group of integers modulo n and let En(k) be the set of all k-element subsets of Zn where 1≤k<n. If E∈En(k), let [E]={E+r:r∈Zn}. Then [E] is the orbit of E where Zn acts on En(k) via (r,E)↦E+r. Furthermore, {[E]:E∈En(k)} is a partition of En(k) into Zn-orbits. In this article, we count the total number of Zn-orbits of En(k), count the number of orbits of each size, determine the corresponding results when fixed points are introduced, and give an application to cyclic and r-pyramidal decompositions of complete uniform hypergraphs into isomorphic subgraphs.

A note on block-and-bridge preserving maximum common subgraph algorithms for outerplanar graphs

Schietgat, Ramon and Bruynooghe [Schietgal et al., AMAI, 2013] proposed a polynomial-time algorithm for computing a maximum common subgraph under the block-and-bridge preserving subgraph isomorphism (BBP-MCS) for outerplanar graphs. We show that the article contains the following errors: The running time of the presented approach is claimed to be $\mathcal{O}(n^{2.5})$ for two graphs of order $n$. We show that the algorithm of the authors allows no better bound than $\mathcal{O}(n^4)$ when using state-of-the-art general purpose methods to solve the matching instances arising as subproblems. This is even true for the special case, where both input graphs are trees. The article suggests that the dissimilarity measure derived from BBP-MCS is a metric. We show that the triangle inequality is not always satisfied and, hence, it is not a metric. Therefore, the dissimilarity measure should not be used in combination with techniques that rely on or exploit the triangle inequality in any way. Where possible, we give hints on techniques that are suitable to improve the algorithm.

GC

We demonstrate a graph caching system GC for expediting subgraph/supergraph queries, which are computationally expensive due to the entailed NP-Complete subgraph isomorphism problem. Unlike existing caching systems for fast data access where each cache hit saves one disk I/O, GC reduces the computational costs due to subgraph isomorphism testing. Moreover, GC harnesses both subgraph and supergraph cache hits, extending the traditional exact-match-only hit, thus resulting in significant speedups. Furthermore, GC features dashboards for both skilled developers and general end-users; the former could investigate and experiment with alternative components/mechanisms while the latter could look into the principle of GC through a number of demonstration scenarios.

A Methodology to Generate Attributed Graphs with a Bounded Graph Edit Distance for Graph-Matching Testing

This paper presents a methodology for generating pairs of attributed graphs with a lower and upper- bounded graph edit distance (GED). It is independent of the type of attributes on nodes and edges. The algorithm is composed of three steps: randomly generating a graph, generating another graph as a sub-graph of the first, and adding structural and semantic noise to both. These graphs, together with their bounded distances, can be used to manufacture synthetic databases of large graphs. The exact GED between large graphs cannot be obtained for runtime reasons since it has to be computed through an optimal algorithm with an exponential computational cost. Through this database, we can test the behavior of the known or new sub-optimal error-tolerant graph-matching algorithms against a lower and an upper bound GED on large graphs, even though we do not have the true distance. It is not clear how the error induced by the use of sub-optimal algorithms grows with problem size. Thus, with this methodology, we can generate graph databases and analyze if the current assumption that we can extrapolate algorithms’ behavior from matching small graphs to large graphs is correct or not. We also show that with some restrictions, the methodology returns the optimal GED in a quadratic time and that it can also be used to generate graph databases to test exact sub-graph isomorphism algorithms.

Two-step approach to scheduling quantum circuits

As the effort to scale up existing quantum hardware proceeds, it becomes necessary to schedule quantum gates in a way that minimizes the number of operations. There are three constraints that have to be satisfied: the order or dependency of the quantum gates in the specific algorithm, the fact that any qubit may be involved in at most one gate at a time, and the restriction that two-qubit gates are implementable only between connected qubits. The last aspect implies that the compilation depends not only on the algorithm, but also on hardware properties like connectivity. Here we suggest a two-step approach in which logical gates are initially scheduled neglecting connectivity considerations, while routing operations are added at a later step in a way that minimizes their overhead. We rephrase the subtasks of gate scheduling in terms of graph problems like edge-coloring and maximum subgraph isomorphism. While this approach is general, we specialize to a one-dimensional array of qubits to propose a routing scheme that is minimal in the number of exchange operations. As a practical application, we schedule the quantum approximate optimization algorithm in a linear geometry and quantify the reduction in the number of gates and circuit depth that results from increasing the efficacy of the scheduling strategies.

Finding and Counting Tree-Like Subgraphs Using MapReduce

Several variants of the subgraph isomorphism problem, e.g., finding, counting, and estimating frequencies of subgraphs in networks arise in a number of real world applications, such as web analysis, disease diffusion prediction, and social network analysis. These problems are computationally challenging in having to scale to very large networks with millions of vertices. In this paper, we present SAHad , a MapReduce algorithm for detecting and counting trees of bounded size using the elegant color coding technique developed by N. Alon et al. SAHad is a randomized algorithm, and we show rigorous bounds on the approximation quality and the performance of it. SAHad scales to very large networks comprising of $10^7-10^8$ vertices and $10^8-10^9$ edges and tree-like (acyclic) templates with up to 12 vertices. Further, we extend our results by implementing SAHad in the Harp framework, which is more of a high performance computing environment. The new implementation gives 100x improvement in performance over the standard Hadoop implementation and achieves better performance than state-of-the-art MPI solutions on larger graphs.

동형 서브그래프 질의 처리를 위한 효율적인 그래프 경로 기반 인덱싱 기법

동형 서브그래프 질의 처리(Subgraph isomorphism query processing)란 대용량의 여러 작은 그래프들 혹은 하나의 큰 그래프로 이루어진 그래프 데이터베이스에 대해 사용자로부터 주어진 질의 그래프와 구조적으로 동일한(isomorphic) 여러 서브그래프들을 찾아주는 과정이다. 기존 연구에서는 그래프 경로(path) 기반 인덱스와 각 경로에 대한 테이블 간 조인(join) 연산을 통해 질의를 처리하는 방법을 제안하였다. 하지만 동일한 구조이거나 공통 에지(edge)를 가지는 경로들의 경우 데이터 그래프에 대한 중복정보를 가져 인덱스의 크기가 불필요하게 커지는 문제점이 있다. 본 논문에서는 패스 코드(path-code)와 유니크 코드를(unique-code)를 이용하여 데이터 그래프에 대한 중복 정보를 제거하는 효율적인 경로 기반 인덱싱 방법을 제안한다. 실험에서는 기존 경로 기반의 인덱싱 방법과 비교하여 제안한 인덱싱 방법의 효율성을 보인다. 또한, 실제 그래프 데이터베이스에 대해 제안한 방법이 빠른 질의 처리를 가짐을 보인다.

Sachem: a chemical cartridge for high-performance substructure search

BackgroundStructure search is one of the valuable capabilities of small-molecule databases. Fingerprint-based screening methods are usually employed to enhance the search performance by reducing the number of calls to the verification procedure. In substructure search, fingerprints are designed to capture important structural aspects of the molecule to aid the decision about whether the molecule contains a given substructure. Currently available cartridges typically provide acceptable search performance for processing user queries, but do not scale satisfactorily with dataset size.ResultsWe present Sachem, a new open-source chemical cartridge that implements two substructure search methods: The first is a performance-oriented reimplementation of substructure indexing based on the OrChem fingerprint, and the second is a novel method that employs newly designed fingerprints stored in inverted indices. We assessed the performance of both methods on small, medium, and large datasets containing 1, 10, and 94 million compounds, respectively. Comparison of Sachem with other freely available cartridges revealed improvements in overall performance, scaling potential and screen-out efficiency.ConclusionsThe Sachem cartridge allows efficient substructure searches in databases of all sizes. The sublinear performance scaling of the second method and the ability to efficiently query large amounts of pre-extracted information may together open the door to new applications for substructure searches.

Using SMILES strings for the description of chemical connectivity in the Crystallography Open Database

Computer descriptions of chemical molecular connectivity are necessary for searching chemical databases and for predicting chemical properties from molecular structure. In this article, the ongoing work to describe the chemical connectivity of entries contained in the Crystallography Open Database (COD) in SMILES format is reported. This collection of SMILES is publicly available for chemical (substructure) search or for any other purpose on an open-access basis, as is the COD itself. The conventions that have been followed for the representation of compounds that do not fit into the valence bond theory are outlined for the most frequently found cases. The procedure for getting the SMILES out of the CIF files starts with checking whether the atoms in the asymmetric unit are a chemically acceptable image of the compound. When they are not (molecule in a symmetry element, disorder, polymeric species,etc.), the previously published cif_molecule program is used to get such image in many cases. The program package Open Babel is then applied to get SMILES strings from the CIF files (either those directly taken from the COD or those produced by cif_molecule when applicable). The results are then checked and/or fixed by a human editor, in a computer-aided task that at present still consumes a great deal of human time. Even if the procedure still needs to be improved to make it more automatic (and hence faster), it has already yielded more than 160,000 curated chemical structures and the purpose of this article is to announce the existence of this work to the chemical community as well as to spread the use of its results.

Answering Natural Language Questions by Subgraph Matching over Knowledge Graphs

RDF question/answering (Q/A) allows users to ask questions in natural languages over a knowledge base represented by RDF. To answer a natural language question, the existing work takes a two-stage approach: question understanding and query evaluation. Their focus is on question understanding to deal with the disambiguation of the natural language phrases. The most common technique is the joint disambiguation, which has the exponential search space. In this paper, we propose a systematic framework to answer natural language questions over RDF repository (RDF Q/A) from a graph data-driven perspective. We propose a semantic query graph to model the query intention in the natural language question in a structural way, based on which, RDF Q/A is reduced to subgraph matching problem. More importantly, we resolve the ambiguity of natural language questions at the time when matches of query are found. The cost of disambiguation is saved if there are no matching found. More specifically, we propose two different frameworks to build the semantic query graph, one is relation (edge)-first and the other one is node-first. We compare our method with some state-of-the-art RDF Q/A systems in the benchmark dataset. Extensive experiments confirm that our method not only improves the precision but also speeds up query performance greatly.

The Descriptive Complexity of Subgraph Isomorphism Without Numerics

Let F be a connected graph with ℓ vertices. The existence of a subgraph isomorphic to F can be defined in first-order logic with quantifier depth no better than ℓ, simply because no first-order formula of smaller quantifier depth can distinguish between the complete graphs Kℓ and Kℓ− 1. We show that, for some F, the existence of an F subgraph in sufficiently large connected graphs is definable with quantifier depth ℓ − 3. On the other hand, this is never possible with quantifier depth better than ℓ/2. If we, however, consider definitions over connected graphs with sufficiently large treewidth, the quantifier depth can for some F be arbitrarily small comparing to ℓ but never smaller than the treewidth of F. Moreover, the definitions over highly connected graphs require quantifier depth strictly more than the density of F. Finally, we determine the exact values of these descriptive complexity parameters for all connected pattern graphs F on 4 vertices.

An oriented feature extraction and recognition approach for concave-convex mixed interacting features in cast-then-machined parts

Feature recognition is an important technology of computer-aided design/computer-aided engineering/computer-aided process planning/computer-aided manufacturing integration in cast-then-machined part manufacturing. Graph-based approach is one of the most popular feature recognition methods; however, it cannot still solve concave-convex mixed interacting feature recognition problem, which is a common problem in feature recognition of cast-then-machined parts. In this study, an oriented feature extraction and recognition approach is proposed for concave-convex mixed interacting features. The method first extracts predefined features directionally according to the rules generated from attributed adjacency graphs–based feature library and peels off them from part model layer by layer. Sub-features in an interacting feature are associated via hints and organized as a feature tree. The time cost is reduced to less than [Formula: see text] by eliminating subgraph isomorphism and matching operations. Oriented feature extraction and recognition approach recognizes non-freeform-surface features directionally regardless of the part structure. Hence, its application scope can be extended to multiple kinds of non-freeform-surface parts by customizing. Based on our findings, implementations on prismatic, plate, fork, axlebox, linkage, and cast-then-machined parts prove that the proposed approach is applicable on non-freeform-surface parts and effectively recognize concave-convex mixed interacting feature in various mechanical parts.