Common Subgraph Research Articles

Graph comparison via nonlinear quantum search

In this paper we present an efficiently scaling quantum algorithm which finds the size of the maximum common edge subgraph for a pair of arbitrary graphs and thus provides a meaningful measure of graph similarity. The algorithm makes use of a two-part quantum dynamic process: in the first part we obtain information crucial for the comparison of two graphs through linear quantum computation. However, this information is hidden in the quantum system with vanishingly small amplitude that even quantum algorithms such as Grover's search are not fast enough to distill the information efficiently. In order to extract the information we call upon techniques in nonlinear quantum computing to provide the speed-up necessary for an efficient algorithm. The linear quantum circuit requires $\mathcal{O}(n^3 \log^3 (n) \log \log (n))$ elementary quantum gates and the nonlinear evolution under the Gross-Pitaevskii equation has a time scaling of $\mathcal{O}(\frac{1}{g} n^2 \log^3 (n) \log \log (n))$, where $n$ is the number of vertices in each graph and $g$ is the strength of the Gross-Pitaveskii non-linearity. Through this example, we demonstrate the power of nonlinear quantum search techniques to solve a subset of NP-hard problems.

Semantic measure of plagiarism using a hierarchical graph model

Traditional plagiarism detection is based primarily on methods of character matching or topic similarity. Another promising methodology remains largely unexplored: employing deep mining to establish a contextual hierarchy among themes. This paper proposes a semantic approach to measuring the extent of plagiarism, based on a hierarchical graph model. The main innovations are as follows: (1) hierarchical extraction of topic feature terms and elucidation of a corresponding graph structure; (2) graph similarity calculation based on the maximum common subgraph. This semantic-measure method goes beyond semantic detection of topics to take into account the context of topic feature terms, as well as the hierarchical structure by which those topics are related. This contextual-hierarchical perspective should, in turn, improve the accuracy of plagiarism detection. In addition, by mining the implicit relationships between hierarchical feature terms, our method can detect plagiarized documents with similar themes but using different topic words: a potential boon to plagiarism detection recall. In an experiment conducted on a dataset from Chinese paper database CNKI, the semantic-measure method indeed demonstrates accuracy and recall superior to those achieved with current state-of-the-art methods.

Ω76: A designed antimicrobial peptide to combat carbapenem- and tigecycline-resistant Acinetobacter baumannii.

Drug resistance is a public health concern that threatens to undermine decades of medical progress. ESKAPE pathogens cause most nosocomial infections, and are frequently resistant to carbapenem antibiotics, usually leaving tigecycline and colistin as the last treatment options. However, increasing tigecycline resistance and colistin's nephrotoxicity severely restrict use of these antibiotics. We have designed antimicrobial peptides using a maximum common subgraph approach. Our best peptide (Ω76) displayed high efficacy against carbapenem and tigecycline-resistant Acinetobacter baumannii in mice. Mice treated with repeated sublethal doses of Ω76 displayed no signs of chronic toxicity. Sublethal Ω76 doses co-administered alongside sublethal colistin doses displayed no additive toxicity. These results indicate that Ω76 can potentially supplement or replace colistin, especially where nephrotoxicity is a concern. To our knowledge, no other existing antibiotics occupy this clinical niche. Mechanistically, Ω76 adopts an α-helical structure in membranes, causing rapid membrane disruption, leakage, and bacterial death.

Structural similarity measure between UML class diagrams based on UCG

In software reuse, the reuse of UML class diagram produced in design phase has received more attention due to the important influence on the following developing process. The reuse is based on similarity. The similarity between class diagrams contains semantic and structural aspects. The existing works focus on semantic similarity, while the structural similarity is little paid attention to. The structure of class diagram can be categorized into two aspects: intra-structure and inter-structure. The intra-structure refers to the composition of each class, and the inter-structure is represented as the relationships between classes. So, the structural similarity measure should be carried out from these two aspects. In this paper, we propose to use a graph named UML class graph (UCG) to represent a class diagram for the structural similarity measure. An algorithm based on UCG Maximum Common Subgraph Sequence is proposed for the inter-structure similarity measure, and UCG edit distance is proposed and introduced to the intra-structure similarity measure. The experimental results show that our proposed approach is effective within a domain or across domains.

Comparing Molecular Patterns Using the Example of SMARTS: Theory and Algorithms.

Molecular patterns are widely used for compound filtering in molecular design endeavors. They describe structural properties that are connected with unwanted physical or chemical properties like reactivity or toxicity. With filter sets comprising hundreds of structural filters, an analytic approach to compare those patterns is needed. Here we present a novel approach to solve the generic pattern comparison problem. We introduce chemically inspired fingerprints for pattern nodes and edges to derive an easy-to-compare pattern representation. On two annotated pattern graphs we apply a maximum common subgraph algorithm enabling the calculation of pattern inclusion and similarity. The resulting algorithm can be used in many different ways. We can automatically derive pattern hierarchies or search in large pattern collections for more general or more specific patterns. To the best of our knowledge, the presented algorithm is the first of its kind enabling these types of chemical pattern analytics. Our new tool named SMARTScompare is an implementation of the approach for the SMARTS language, which is the quasi-standard for structural filters. We demonstrate the capabilities of SMARTScompare on a large collection of SMARTS patterns from real applications.

A fast discovery algorithm for large common connected induced subgraphs

We present a fast algorithm for the classical problem of finding common subgraphs, which are useful for detecting structural relationships between biological macromolecules. Although the cost is potentially high for this hard problem, we improve performance by several orders of magnitude compared to known algorithms. We validate our findings with experiments on proteins with thousands of atoms.

Unsupervised graph-based rank aggregation for improved retrieval

This paper presents a robust and comprehensive graph-based rank aggregation approach, used to combine results of isolated ranker models in retrieval tasks. The method follows an unsupervised scheme, which is independent of how the isolated ranks are formulated. Our approach is able to combine arbitrary models, defined in terms of different ranking criteria, such as those based on textual, image or hybrid content representations.We reformulate the ad-hoc retrieval problem as a document retrieval based on fusion graphs, which we propose as a new unified representation model capable of merging multiple ranks and expressing inter-relationships of retrieval results automatically. By doing so, we claim that the retrieval system can benefit from learning the manifold structure of datasets, thus leading to more effective results. Another contribution is that our graph-based aggregation formulation, unlike existing approaches, allows for encapsulating contextual information encoded from multiple ranks, which can be directly used for ranking, without further computations and post-processing steps over the graphs. Based on the graphs, a novel similarity retrieval score is formulated using an efficient computation of minimum common subgraphs. Finally, another benefit over existing approaches is the absence of hyperparameters.A comprehensive experimental evaluation was conducted considering diverse well-known public datasets, composed of textual, image, and multimodal documents. Performed experiments demonstrate that our method reaches top performance, yielding better effectiveness scores than state-of-the-art baseline methods and promoting large gains over the rankers being fused, thus demonstrating the successful capability of the proposal in representing queries based on a unified graph-based model of rank fusions.

On multi-consensus and almost equitable graph partitions

This paper deals with multi-consensus in multi-agent systems, focusing on the relationship between multi-consensusability and the underlying digraph topology. In particular, the topological arrangement of the network nodes naturally suggests distinguishing among, on the one hand, separate independent groups of agents agreeing internally and, on the other hand, a dependent common subgraph whose internal consensuses can be computed as a convex combination of the different consensuses achieved by the previously mentioned independent groups. The distinct achieved consensuses are as many as the number of groups of agents defining cells of a suitable almost equitable partition. Despite the notational complexity, the related computations are quite simple to carry out, as shown in some examples.

Couple Approach to Fixture Design Based on Maximum Common Subgraph Mining and Fixturing Performance Analysis

Couple Approach to Fixture Design Based on Maximum Common Subgraph Mining and Fixturing Performance Analysis

Visual graph mining for graph matching

In this study, we formulate the concept of “mining maximal-size frequent subgraphs” in the challenging domain of visual data (images and videos). In general, visual knowledge can usually be modeled as attributed relational graphs (ARGs) with local attributes representing local parts and pairwise attributes describing the spatial relationship between parts. Thus, from a practical perspective, such mining of maximal-size subgraphs can be regarded as the discovery of common objects from visual data without given annotations of object bounding boxes. From a theoretical perspective, in this study, we propose a generic definition of common subgraphs among ARGs. Many previous studies can be roughly considered as special cases of the definition. In our definition, we consider 1) variations of unary/pairwise attributes among different ARGs, 2) linkage conditions of different nodes, and 3) the learning of similarity metrics for each node. The generality of our subgraph pattern proposes great challenges to the graph-mining algorithm. We propose an approximate but efficient solution to the mining problem. We conduct five experiments to evaluate our method with different kinds of visual data, including videos and RGB/RGB-D images. These experiments demonstrate the generality of the proposed method.

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.

An automatic personalized internal fixation plate modeling framework for minimally invasive long bone fracture surgery based on pre-registration with maximum common subgraph strategy

In this paper, a visualization and modeling method for the internal fixation plate in personalized and minimally invasive long bone fracture surgery is presented. This framework mainly includes six sub-steps: firstly, the Principal Component Analysis (PCA) method is used to extract the 3D axis of the broken bone; secondly, the Gauss mapping method is utilized to segment the end surfaces of the broken bone; thirdly, the maximum common subgraph strategy is utilized to complete the end surface matching; fourthly, the OBB (Oriented Bounding Box) method is utilized to accomplish the pre-registration of the fracture surface; fifthly, the ICP (Iterative Closest Point) algorithm is utilized to achieve the fracture surface models’ accurate alignment; lastly, the personalized bent internal fixation plate model can be reconstructed based on anchor points. Via this method, doctors can obtain the accurate and personalized internal fixation plate model that has the best matching geometric form to the patient’s broken bones. This method can provide a well technique base and computational solution for the minimally invasive long bone fracture surgery.

Gluing of graph Laplacians and their spectra

ABSTRACTWe study two different types of gluing for graphs: interface (obtained by choosing a common subgraph as the gluing component) and bridge gluing (obtained by adding a set of edges to the given subgraphs). We introduce formulae for computing even and odd Laplacians of graphs obtained by gluing, as well as their spectra. We subsequently discuss applications to quantum mechanics and bounds for the Fiedler value of the gluing of graphs.

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.

Dual Graph Partitioning Highlights a Small Group of Pseudoknot-Containing RNA Submotifs.

RNA molecules are composed of modular architectural units that define their unique structural and functional properties. Characterization of these building blocks can help interpret RNA structure/function relationships. We present an RNA secondary structure motif and submotif library using dual graph representation and partitioning. Dual graphs represent RNA helices as vertices and loops as edges. Unlike tree graphs, dual graphs can represent RNA pseudoknots (intertwined base pairs). For a representative set of RNA structures, we construct dual graphs from their secondary structures, and apply our partitioning algorithm to identify non-separable subgraphs (or blocks) without breaking pseudoknots. We report 56 subgraph blocks up to nine vertices; among them, 22 are frequently occurring, 15 of which contain pseudoknots. We then catalog atomic fragments corresponding to the subgraph blocks to define a library of building blocks that can be used for RNA design, which we call RAG-3Dual, as we have done for tree graphs. As an application, we analyze the distribution of these subgraph blocks within ribosomal RNAs of various prokaryotic and eukaryotic species to identify common subgraphs and possible ancestry relationships. Other applications of dual graph partitioning and motif library can be envisioned for RNA structure analysis and design.

A Fixture Design Retrieving Method Based on Constrained Maximum Common Subgraph

Fixtures are widely used in almost any modern manufacturing. They add directly to the cost base, impact manufacturing firms’ responsiveness and contribute to the overall product quality. Computer-aided intelligent fixture design was developed over the years to give a competitive edge to the manufacturing firms who are facing unprecedented competition and challenges. Among the techniques, case-based reasoning (CBR) method leverages previous design experience and emerged as one of the most popular methods. However, existing CBR methods are more focused on frame work building and less on detailed techniques on case retrieving, which is the central part of any CBR methods. This would inevitably impose negative impact on the overall efficiency of any CBR-based methods. In light of this, this paper presents a new case retrieving method based on a constrained common subgraph technique. This technique tracks down similar cases from a case library through comparing the maximal common subgraphs constrained by meeting fixturing functional requirement. Efficient and robust algorithms have been developed subsequently to implement this technique. The developed method can be highly effective for retrieving cases related to some manufacturing parts with complex geometry. An illustrative example, combined with other key fixture design factors, demonstrates the effectiveness of the proposed method. The presented method is intuitive and can be used in combination with existing CBR methods and well positioned for the upcoming “big data” manufacturing. Note to Practitioners —Providing capability for rapid responsiveness, enhancement of product quality, and production at low cost are the three main objectives for the wide manufacturing firms. Fixtures are widely used across manufacturing and assembly processes, and they are closely linked to all these three objectives. Today’s manufacturing enterprises face unprecedented challenges to control costs and to deal with an ever increasing number of product variants and smaller lot sizes. All these facts raise high demands on computer-aided intelligent fixture design. Case-based reasoning (CBR) method, tackling new problem by using the solution of similar past problems or through revising the previous solution, gains popularity among researchers and practitioners. However, existing CBR methods put more focus on CBR framework design while the case retrieving, the key process of any CBR methods, still relies on some basic feature attributes comparison. This would inevitably reduce the overall effectiveness of the CBR method. In view of that, this paper proposed a graph method for case retrieval based on comparing maximal common subgraphs (MCSs). Dictated by fixture functional requirement, a constraint (to match machining features and/or other user defined requirement) has been imposed during the MCS search process. This constraint turns out to be quite useful in term of reducing search space and increasing computation efficiency. Robust algorithms have been subsequently developed to implement this technique. Graph is a powerful tool to analyze structured object, the proposed method can handle some bespoke and complex fixture design cases. The presented method is intuitive and flexible and can be integrated into existing CBR frameworks to improve the allover effectiveness of current intelligent fixture design.

Efficient graph pattern matching framework for network-based in-vehicle fault detection

Abnormal messages propagated from faulty operations in an in-vehicle network may severely harm a vehicular system, but they cannot be easily detected when their information is not known in advance. To support an efficient detection of faulty message patterns propagated in the in-vehicle network, this paper presents a novel graph pattern matching framework built upon a message log-driven graph modeling. Our framework models the unknown operation of the in-vehicle network as a query graph and the reference database of normal operations as data graphs. Given a query graph and data graphs, we determine whether the query graph represents normal or fault operation by using the distance measure on the data graphs. The analysis of the faulty message propagation requires to consider the sequence of events in the distance measure, and thus, using the conventional graph distance measures can generate false negatives due to the lack of consideration of the sequence relationships among the events. We therefore propose a novel distance metric based on the maximum common subgraph (MCS) between two graphs and the sequence numbers of messages, which works robustly even for the abnormal faulty patterns and can avoid false negatives in large databases. Since the problem of MCS computation is NP-hard, we also propose two efficient filtering techniques, one based on the lower bound of the MCS distance for a polynomial-time approximation and the other based on edge pruning. Experiments performed on real and synthetic datasets to assess our framework show that ours significantly outperforms the previously existing methods in terms of both performance and accuracy of query responses.

A common subgraph correspondence mining framework for map search services

With the development of GPS, Internet, and mobile devices, the map searching services become an essential application in people’s lives. However, existing map searching services only support simple keywords based location search, which neglect users’ complex search requirements, such as searching a hotel surrounded by station, shopping mall, cinema, etc. In this paper, we propose a map searching framework which maps users’ complex search requirements into a graph pattern match problem. In this framework, the user’s query requirements are mapped into a undirected graph, where the vertexes indicate the searched locations, and the edges represent the distance between connected locations. In this way, we propose a common pattern searching algorithm to give the top k matches groups and arrange them using a similarity. The similarity is defined by multi-model information, i.e., the graph structure, location categories, review stars, and review counts. Moreover, this method also allows user to input ambiguous and uncertain query condition with sketching query map. To adapt the method to large-scale data, we also filter the candidate groups by effective pruning methods. The evaluations on Yelp dataset demonstrate the proposed method is effective and flexibility in both certain and uncertain query graphs.

On the NP-hardness of GRacSim drawing and k-SEFE Problems

We study the complexity of two problems on simultaneous graph drawing. The first problem, $\rm{GR{\small AC} S{\small IM~DRAWING}}$, asks for finding a simultaneous geometric embedding of two planar graphs, sharing a common subgraph, such that only crossings at right angles are allowed, and every crossing must involve a private edge of one graph and a private edge of the other graph. The second problem, $k-\rm{SEFE}$, is a restricted version of the topological simultaneous embedding with fixed edges ($\rm{SEFE}$) problem, for two planar graphs, in which every private edge may receive at most $k$ crossings, where $k$ is a prescribed positive integer. We show that $\rm{GR{\small AC} S{\small IM~DRAWING}}$ is $\mathcal{NP}$-hard and that $k-\rm{SEFE}$ is $\mathcal{NP}$-complete. The $\mathcal{NP}$-hardness of both problems is proved using two similar reductions from $\rm{3-P\small{ARTITION}}$.

On maximum common subgraph problems in series–parallel graphs

The complexity of the maximum common connected subgraph problem in partial k-trees is still not fully understood. Polynomial-time solutions are known for degree-bounded outerplanar graphs, a subclass of the partial 2-trees. On the other hand, the problem is known to be NP-hard in vertex-labeled partial 11-trees of bounded degree. We consider series–parallel graphs, i.e., partial 2-trees. We show that the problem remains NP-hard in biconnected series–parallel graphs with all but one vertex of degree 3 or less. A positive complexity result is presented for a related problem of high practical relevance which asks for a maximum common connected subgraph that preserves blocks and bridges of the input graphs. We present a polynomial time algorithm for this problem in series–parallel graphs, which utilizes a combination of BC- and SP-tree data structures to decompose both graphs.