Isomorphism Detection Research Articles

Scripting Language for Java Source Code Recognition

This paper presents general results on the Java source code snippet detection problem. We propose the tool which uses graph and subgraph isomorphism detection. A number of solutions for all of these tasks have been proposed in the literature. However, although that all these solutions are really fast, they compare just the constant static trees. Our solution offers to enter an input sample dynamically with the Scripthon language while preserving an acceptable speed. We used several optimizations to achieve very low number of comparisons during the matching algorithm.

A New Approach for Isomorphism Identification among Compound Kinematic Chains and Mechanisms

Structure synthesis of mechanisms is a pivotal issue in the field of mechanical innovation and mechanical conceptual design. The present work deals with problem of detection of isomorphism which is frequently encountered in structural synthesis of kinematic chains. A new approach based on a combination of eigenvalues and eigenvectors which are further associated with the modified adjacency matrix is proposed. The proposed method not only effective but also more efficient than that are based on the adjacency matrices and capable of detecting isomorphism in all types of compound KC, i.e. chains of single or multi degree of freedom with simple or multiple joints. This study will help the designer to select the best KC and mechanisms to perform the specified task at conceptual stage of design. Some examples are provided to demonstrate the effectiveness of this method.

QuateXelero: An Accelerated Exact Network Motif Detection Algorithm

Finding motifs in biological, social, technological, and other types of networks has become a widespread method to gain more knowledge about these networks’ structure and function. However, this task is very computationally demanding, because it is highly associated with the graph isomorphism which is an NP problem (not known to belong to P or NP-complete subsets yet). Accordingly, this research is endeavoring to decrease the need to call NAUTY isomorphism detection method, which is the most time-consuming step in many existing algorithms. The work provides an extremely fast motif detection algorithm called QuateXelero, which has a Quaternary Tree data structure in the heart. The proposed algorithm is based on the well-known ESU (FANMOD) motif detection algorithm. The results of experiments on some standard model networks approve the overal superiority of the proposed algorithm, namely QuateXelero, compared with two of the fastest existing algorithms, G-Tries and Kavosh. QuateXelero is especially fastest in constructing the central data structure of the algorithm from scratch based on the input network.

Isomorphism detection of kinematic chains based on the improved circuit simulation method

A new method for isomorphism detection based on circuit simulation is presented in this paper. Further, the circuit simulation method is applied to the detection of isomorphic kinematic chains. The proposed method as well as some existing methods has been tested on a large number of kinematic chains, and comparison between these methods has been made. The results showed that the circuit simulation method is more effective in the determination of the correspondence between links and more efficient in the detection of the isomorphism of large-scale kinematic chains.

Isomorphism-Aware Identification of Custom Instructions With I/O Serialization

Extensible processors have been widely used to achieve the conflicting demands for performance improvement, low power consumption, and flexibility. As extensible processors have become more popular, several algorithms have been proposed for automatically identifying instruction-set extensions in order to reduce the effort of manual design and verification. However, most of them focus on finding large and complex instructions that are used only once, rather than repeatedly used ones. Moreover, some other approaches that consider recurrence are limited to finding small instructions. This paper proposes a novel algorithm that considers the instruction reusability as well as input/output (I/O) serialization. In order to overcome the high complexity of the problem, we develop a canonical-form construction algorithm for fast isomorphism detection on directed acyclic graphs and an incremental template generation algorithm that identifies the best custom instruction in terms of a user-defined fitness function. Moreover, our algorithm serializes I/O operations so that the numbers of inputs and outputs of custom instructions are not limited by the microarchitecture. This paper also proposes an algorithm for multiple custom instructions utilizing a well-known iterative selection algorithm. Last, it presents a hybrid algorithm composed of our algorithm and the previous algorithm that does not consider reusability. Experimental results show that our isomorphism-aware algorithm achieves significant improvement over previous approaches in terms of algorithm runtime, as well as performance gain obtained by custom instructions.

Graph Matching Algorithm-Through Isomorphism Detection

This Paper delivers a new algorithm to the problem of graph isomorphism detection. Basically this method is designed in such a way that, a model graph which is known prior is compared with an unknown graph called input graph. Now the problem to be solved is to find a graph isomorphism from the input graph which is given online with the one which is known as model graph. At dynamic time the input graph is compared with the entire model graph for which there exists a graph isomorphism from the input graph are detected. The time complexity depends on the number of input graphs given and size of the graphs. Furthermore it is independent of number of model graphs given and the number of edges in any of the graph.

Methodological Control Framework and Scheduling Algorithm for Internet

Proper control model of the Internet is crucial in network control and management. In this paper, we presented a methodological control framework to describe general process logic and dataflow of network control, which could obtain consistent and global network view on elaborate resource data and network state. As for its scheduling problem, we found that it shares features with virtual network embedding problem if control request appears as a graph of atomic network control action. Inspired by this, we designed an algorithm for the scheduling problem of control request in the Internet based on isomorphic subgraph detection. Furthermore, we also discussed control action migration under measuring revenue and cost. Finally, we evaluated the performance of our proposed algorithm with different parameters by simulation experiments.

Faster subgraph isomorphism detection by well-founded total order indexing

In this paper an extension to index-based subgraph matching is proposed. This extension significantly speeds up the indexing time for graphs where the nodes are labeled with a rather small amount of different classes. Furthermore, the needed storage amount is significantly reduced. In order to reduce the complexity, we introduce a weight function for labeled graphs. Using this weight function, a well-founded total order is defined on the weights of the labels. Inversions which violate the order are not allowed. A computational complexity analysis of the new preprocessing is given and its completeness is proven. Furthermore, in a number of practical experiments with randomly generated graphs the improvement of the new approach is shown. In experiments performed on random sample graphs, and on real-world datasets. The number of permutations for the real-world datasets have been decreased to a fraction of 10−5 and 10−8 in average compared to the original approach by Messmer. The novel indexing strategy makes indexing of larger graphs feasible, allowing for fast detection of subgraphs.

Modified joint connectivity approach for identification of topological characteristics of planar kinematic chains

In a kinematic chain, the links are connected to each other through joints. The connectivity of a joint indicates the number of joints to which it is connected. The connectivity level of a joint indicates the distance by which it is separated from the adjacent joints. The concept of joint connectivity and its application to detect isomorphism among kinematic chains and their inversions has been already reported by authors. The method utilizes the connectivity of joints at different levels to detect isomorphism and inversions among planar kinematic chains. The method is applied to eight-, nine-, and ten-link planar kinematic chains. The results so obtained are in agreement with those available in the literature. In this study, the method is further improved by incorporating the type of joint to make it more effective for the detection of isomorphism and distinct inversions. A joint connectivity table completely representing the kinematic chain is proposed. The application of the method is extended for the determination of additional topological characteristics of chains such as categorization of kinematic chains and selection of preferred frame, input and output links for function and path generation. The concept of ‘Motion Transfer Ability’ is introduced and utilized to develop numerical measures for comparing and categorizing the chains at the synthesis stage of mechanism design for a specific application. The method was successfully tested on planar kinematic chains with single and multiple degrees of freedom and the results for eight- and nine-link kinematic chains are appended.

A Novel Algorithm for Enumeration of the Planetary Gear Train Based on Graph Theory

As well known, graph theory is a powerful tool for mechanism design. The enumeration of planet gear trains can be converted the synthesis of graphs while a planetary gear train is converted to a graph. During the enumeration of graphs, the problem of isomorphism should be solved. This paper proposes a novel algorithm used to generate non-isomorphism graphs and thereby omits the part of isomorphism detection. The vertex characteristic is firstly defined in this paper that is the core of the enumeration algorithm. This paper also gives an example of the application for the algorithm.

A method for identification of isomorphism and structural properties of kinematic chains

The present work deals with the structural analysis and synthesis of kinematic chains of mechanisms and robot manipulators. Four key problems, detection of isomorphism among kinematic chain, identification of isomorphism among inversions of given kinematic chain, identification of rigid sub-chain and type of degree of freedom of kinematic chains are considered. A method based on the flow path matrices of kinematic chains is proposed and two new structural invariants, sum of the absolute values of the characteristic polynomial coefficients (SCPC) and maximum absolute value of the characteristic polynomial coefficient (MCPC) are determined using software MATLAB. These invariants are used as the composite identification number of a kinematic chain and mechanisms. The advantage of this method is that it covers all planar kinematic chains of one, two and three degree of freedom at once for identification of isomorphism and for structural properties.

Matching Relationship between Frequency Characteristic and Parasitic Error of Compliant Linear Buffer Mechanism

A novel compliant linear buffer mechanism (CLBM) is designed for impact isolation. In view of the incompatible relationship between frequency characteristic and parasitic error of compliant linear mechanism, the mixed compliant linear mechanism(MCLM) is proposed by combining the Lumped Compliant Mechanism(LCM) and the Distributed Compliant Mechanism(DCM).The topology matrices for four kinds of parallelogram linear compliant mechanisms are built through the method of type synthesis. The characteristic polynominal (CP) for the compliant mechanism matrices[CM] are calculated for the isomorphism detection of compliant mechanism. The finite element analysis (FEA) model of these four kinds of linear compliant mechanism is built to complete numerical analysis on the structure frequency and parasitic error with different sizes, and the relationship between the frequency characteristic and parasitic error of the compliant linear mechanism is found out. MatlabTM software is used to obtain the functional formulas by the method of polynomial curve fitting (PCF) for The FEA results show that the structure configuration of MCLM can achieve a higher structure frequency and a greater kinetic precision over the pure LCM and DCM at the same time, and also indicates that the analysis method of frequency characteristic and parasitic error for compliant mechanism is efficient and should be effective on the structure optimization of the novel CLBM.

Superior estimation abilities in two autistic spectrum children

Anecdotal reports of superior estimation abilities in autistic individuals (e.g., Sacks, 1985) have never been confirmed empirically. We present here case studies of 2 children with autistic spectrum diagnoses and report remarkable abilities in estimation for several quantifiable dimensions. K.T. and G.T. were tested at 9 years of age for estimation of rank, numerosity, time, weight, length, surface, distance, and precise enumeration for small numbers. Their performances were compared to those of 6 age- and IQ- matched comparison children. K.T. demonstrated a superior level of performance in estimating rank (e.g., which set has larger numerosity?) but his performance in other tasks was average. G.T. displayed outstanding performance in estimating numerosity, time, weight, surface, length, and distance, with average performance in other tasks. These results show that certain autistic spectrum individuals may develop superior and highly specialized abilities in estimation. We discuss these findings in relation to the role of “veridical mapping” in the development of special ability (Mottron, Dawson, & Soulières, 2009; Mottron, Dawson, Soulieres, Hubert, & Burack, 2006a). Veridical mapping is the detection of isomorphism within a code, between two codes, or between one code and isomorphic elements of the world. Within this framework, it is proposed that estimation abilities, like absolute pitch, rely on the ability to map a verbal code with a specific magnitude of a psychophysical dimension.

Application of link adjacency values to detect isomorphism among kinematic chains

The present work deals with problem of detection of isomorphism which is frequently encountered in structural synthesis of kinematic chains. A new method has been proposed using two invariants called as First adjacency chain link string [FACLS] and Second adjacency chain link string [SACLS]. These invariants take into account the degree of links and type of joints and are used as the composite identification number of a KC. The proposed method is easy to compute, reliable and capable of detecting isomorphism in all types of compound KC, i.e. chains of single or multi degree of freedom with simple or multiple joints. This study will help the designer to select the best KC and mechanisms to perform the specified task at conceptual stage of design. Some examples are provided to demonstrate the effectiveness of this method.

Description and Application of Similarity‐Based Methods for Fast and Simple QSAR Model Development

AbstractA molecular similarity‐based approximation to fast methodologies for developing QSAR models is presented in this paper with the aim of evaluating reliability of different similarity proposals. Inhibition of carbonic anhydrase presented by a dataset of 47 sulfonamides was the chemical framework employed to build QSAR models. A view of different chemical isomorphism extraction methods, similarity metrics, and structural difference‐based approaches is given in order to provide pharmacological chemists with fast modeling and predictive tools. Recent isomorphism detection approaches which account for dissimilarity between border atoms and bonds were also employed to analyze differences involved in scaffold substitution positions. Thus, the compounds characterization attending to several chemical criteria has been studied by principal component analysis and prediction of the inhibitory activity was carried out by partial least squares regression processes. Fingerprint‐based and approximate similarities gave the best statistical results (Q2>0.70). The latter demonstrated to be useful to detect anomalous behavior presented by very similar molecules which show very different activities. External validations (test r2≈0.90) were also carried out in order to evaluate predictions obtained for molecules which have not participated in the fitting stage.

New Method to Detect Isomorphism in Kinematic Chains

The present work deals with the problem of detection of isomorphism, which is frequently encountered in structural synthesis of kinematic chains (KC). A new method based on theoretic approach, easy to compute and reliable is suggested in this paper. The KC are represented in the form of the Joint-Joint [JJ] matrices. Two structural invariants derived from the characteristic polynomials of the [JJ] matrix of the KC are the sum of absolute characteristic polynomial coefficients (shortened as ΣJJ) and maximum absolute value of the characteristic polynomial coefficient (shortened as MJJ). These invariants are used as the composite identification number of a KC and mechanisms. It is capable of detecting isomorphism in all types of planar kinematic chains. This study will help the designer to select the best KC and mechanisms to perform the specified task and avoid duplication at the conceptual stage of design. The application this study is in research and development industries. The proposed method has been explained with the help of examples. The KC of 1-F, 8-links, and 10-links as well as 2-F, 9-link has been tested and the results are in complete agreement with the available literature of structural synthesis.

Improving Neural Networks for Mechanism Kinematic Chain Isomorphism Identification

Detection of isomorphism among kinematic chains is essential in mechanical design, but difficult and computationally expensive. It has been shown that both traditional methods and previously presented neural networks still have a lot to be desired in aspects such as simplifying procedure of identification and adapting automatic computation. Therefore, a new algorithm based on a competitive Hopfield network is developed for automatic computation in the kinematic chain isomorphism problem. The neural approach provides directly interpretable solutions and does not demand tuning of parameters. We have tested the algorithm by solving problems reported in the recent mechanical literature. Simulation results show the effectiveness of the network that rapidly identifies isomorphic kinematic chains.

An automated method for type synthesis of planar linkages based on a constrained subgraph isomorphism detection

We present a method to enumerate and codify all non-isomorphic solutions, for the problem of synthesizing the type of single-DOF linkage mechanisms that satisfy structural requirements for a given kinematic problem. The method is based on the construction of an “initial graph” taking into account prescribed parts (such as fixations, moving bodies, joints and their interconnections) and the kinematic constraints imposed on them. This initial graph containing structural characteristics of the problem is used as a pattern to search inside a selected atlas of one-DOF mechanism also represented by graphs. A new graph-matrix representation of mechanisms and a mechanism identifier based on the degree code concept was developed to avoid isomorphic occurrences of the initial graph inside each mechanism of the atlas. The same tools were used to enumerate various atlases specialized in a non-isomorphic way from basic kinematic chains. This enumeration takes into account different types of links (rigid, flexible) and joints (revolute, prismatic, flexible, clamped), and proper restrictions were designed to avoid kinematically invalid topologies. The methodology is illustrated with examples for several kinematic tasks.

QSAR models based on isomorphic and nonisomorphic data fusion for predicting the blood brain barrier permeability

A QSAR model for predicting the blood brain barrier permeability (BBBP) in a large and heterogeneous variety of compounds (136 compounds) has been developed using approximate similarity (AS) matrices as predictors and PLS as multivariate regression technique. AS values fuse information of both the isomorphic similarity and nonisomorphic dissimilarity with the purpose of achieving an accurate predictive space. In addition to the fact of applying AS values to heterogeneous data sets, a new concept on graph isomorphism based on the extended maximum common subgraph (EMCS) is defined for the building of AS spaces considering the atoms and bonds, which are bridges between the isomorphic and nonisomorphic substructures. This new isomorphism detection has as objective to take into account the position and nature of the nucleus substituents, thus allowing the development of accurate models for large and diverse sets of compounds. After an outliers study, the training and test stages were made and the results obtained using several AS approaches were compared. Several validation processes were carried out by means of employing several test sets, and high predictive ability was obtained for all the cases (Q(2) = 0.81 and standard error in prediction, SEP = 0.29).

Structural synthesis of planar kinematic chains by adapting a Mckay-type algorithm

Synthesis of kinematic chains can be viewed as the enumeration of a certain class of graphs. Very efficient algorithms, using group theoretic techniques, exist for exhaustive isomorph-free generation of certain classes of combinatorial objects, which either eliminate or restrict the explicit isomorphism detection. An algorithm belonging to one particular class called McKay-type, in combination with an efficient degeneracy testing algorithm, is used for the synthesis of planar mechanisms. The existing results are reexamined and the discrepancies are reconciled.