Search results for: Graph Query
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 473

Search results for: Graph Query

413 Spanning Tree Transformation of Connected Graphs into Single-Row Networks

Authors: S.L. Loh, S. Salleh, N.H. Sarmin

Abstract:

A spanning tree of a connected graph is a tree which consists the set of vertices and some or perhaps all of the edges from the connected graph. In this paper, a model for spanning tree transformation of connected graphs into single-row networks, namely Spanning Tree of Connected Graph Modeling (STCGM) will be introduced. Path-Growing Tree-Forming algorithm applied with Vertex-Prioritized is contained in the model to produce the spanning tree from the connected graph. Paths are produced by Path-Growing and they are combined into a spanning tree by Tree-Forming. The spanning tree that is produced from the connected graph is then transformed into single-row network using Tree Sequence Modeling (TSM). Finally, the single-row routing problem is solved using a method called Enhanced Simulated Annealing for Single-Row Routing (ESSR).

Keywords: Graph theory, simulated annealing, single-rowrouting and spanning tree.

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412 Model Inversion of a Two Degrees of Freedom Linearized PUMA from Bicausal Bond Graphs

Authors: Gilberto Gonzalez-A, Ignacio Rodríguez- A., Dunia Nuñez-P

Abstract:

A bond graph model of a two degrees of freedom PUMA is described. System inversion gives the system input required to generate a given system output. In order to get the system inversion of the PUMA manipulator, a linearization of the nonlinear bond graph is obtained. Hence, the bicausality of the linearized bond graph of the PUMA manipulator is applied. Thus, the bicausal bond graph provides a systematic way of generating the equations of the system inversion. Simulation results to verify the calculated input for a given output are shown.

Keywords: Bond graph, system inversion, bicausality, PUMA manipulator

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411 Concurrency in Web Access Patterns Mining

Authors: Jing Lu, Malcolm Keech, Weiru Chen

Abstract:

Web usage mining is an interesting application of data mining which provides insight into customer behaviour on the Internet. An important technique to discover user access and navigation trails is based on sequential patterns mining. One of the key challenges for web access patterns mining is tackling the problem of mining richly structured patterns. This paper proposes a novel model called Web Access Patterns Graph (WAP-Graph) to represent all of the access patterns from web mining graphically. WAP-Graph also motivates the search for new structural relation patterns, i.e. Concurrent Access Patterns (CAP), to identify and predict more complex web page requests. Corresponding CAP mining and modelling methods are proposed and shown to be effective in the search for and representation of concurrency between access patterns on the web. From experiments conducted on large-scale synthetic sequence data as well as real web access data, it is demonstrated that CAP mining provides a powerful method for structural knowledge discovery, which can be visualised through the CAP-Graph model.

Keywords: concurrent access patterns (CAP), CAP mining and modelling, CAP-Graph, web access patterns (WAP), WAP-Graph, Web usage mining.

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410 Formal Modeling and Verification of Software Models

Authors: Siamak Rasulzadeh

Abstract:

Graph transformation has recently become more and more popular as a general visual modeling language to formally state the dynamic semantics of the designed models. Especially, it is a very natural formalism for languages which basically are graph (e.g. UML). Using this technique, we present a highly understandable yet precise approach to formally model and analyze the behavioral semantics of UML 2.0 Activity diagrams. In our proposal, AGG is used to design Activities, then using our previous approach to model checking graph transformation systems, designers can verify and analyze designed Activity diagrams by checking the interesting properties as combination of graph rules and LTL (Linear Temporal Logic) formulas on the Activities.

Keywords: UML 2.0 Activity, Verification, Model Checking, Graph Transformation, Dynamic Semantics.

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409 Towards an Extended SQLf: Bipolar Query Language with Preferences

Authors: L. Ludovic, R. Daniel, S-E Tbahriti

Abstract:

Database management systems that integrate user preferences promise better solution for personalization, greater flexibility and higher quality of query responses. This paper presents a tentative work that studies and investigates approaches to express user preferences in queries. We sketch an extend capabilities of SQLf language that uses the fuzzy set theory in order to define the user preferences. For that, two essential points are considered: the first concerns the expression of user preferences in SQLf by so-called fuzzy commensurable predicates set. The second concerns the bipolar way in which these user preferences are expressed on mandatory and/or optional preferences.

Keywords: Flexible query language, relational database, userpreference.

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408 Database Placement on Large-Scale Systems

Authors: Cherif Haddad, Faouzi Ben Charrada

Abstract:

Large-scale systems such as Grids offer infrastructures for both data distribution and parallel processing. The use of Grid infrastructures is a more recent issue that is already impacting the Distributed Database Management System industry. In DBMS, distributed query processing has emerged as a fundamental technique for ensuring high performance in distributed databases. Database placement is particularly important in large-scale systems because it reduces communication costs and improves resource usage. In this paper, we propose a dynamic database placement policy that depends on query patterns and Grid sites capabilities. We evaluate the performance of the proposed database placement policy using simulations. The obtained results show that dynamic database placement can significantly improve the performance of distributed query processing.

Keywords: Large-scale systems, Grid environment, Distributed Databases, Distributed query processing, Database placement

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407 Hamiltonian Factors in Hamiltonian Graphs

Authors: Sizhong Zhou, Bingyuan Pu

Abstract:

Let G be a Hamiltonian graph. A factor F of G is called a Hamiltonian factor if F contains a Hamiltonian cycle. In this paper, two sufficient conditions are given, which are two neighborhood conditions for a Hamiltonian graph G to have a Hamiltonian factor.

Keywords: graph, neighborhood, factor, Hamiltonian factor.

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406 A Review on Important Aspects of Information Retrieval

Authors: Yogesh Gupta, Ashish Saini, A.K. Saxena

Abstract:

Information retrieval has become an important field of study and research under computer science due to explosive growth of information available in the form of full text, hypertext, administrative text, directory, numeric or bibliographic text. The research work is going on various aspects of information retrieval systems so as to improve its efficiency and reliability. This paper presents a comprehensive study, which discusses not only emergence and evolution of information retrieval but also includes different information retrieval models and some important aspects such as document representation, similarity measure and query expansion.

Keywords: Information Retrieval, query expansion, similarity measure, query expansion, vector space model.

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405 On Chvátal’s Conjecture for the Hamiltonicity of 1-Tough Graphs and Their Complements

Authors: Shin-Shin Kao, Yuan-Kang Shih, Hsun Su

Abstract:

In this paper, we show that the conjecture of Chv tal, which states that any 1-tough graph is either a Hamiltonian graph or its complement contains a specific graph denoted by F, does not hold in general. More precisely, it is true only for graphs with six or seven vertices, and is false for graphs with eight or more vertices. A theorem is derived as a correction for the conjecture.

Keywords: Complement, degree sum, Hamiltonian, tough.

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404 Natural Language Database Interface for Selection of Data Using Grammar and Parsing

Authors: N. D. Karande, G. A. Patil

Abstract:

Databases have become ubiquitous. Almost all IT applications are storing into and retrieving information from databases. Retrieving information from the database requires knowledge of technical languages such as Structured Query Language (SQL). However majority of the users who interact with the databases do not have a technical background and are intimidated by the idea of using languages such as SQL. This has led to the development of a few Natural Language Database Interfaces (NLDBIs). A NLDBI allows the user to query the database in a natural language. This paper highlights on architecture of new NLDBI system, its implementation and discusses on results obtained. In most of the typical NLDBI systems the natural language statement is converted into an internal representation based on the syntactic and semantic knowledge of the natural language. This representation is then converted into queries using a representation converter. A natural language query is translated to an equivalent SQL query after processing through various stages. The work has been experimented on primitive database queries with certain constraints.

Keywords: Natural language database interface, representation converter, syntactic and semantic knowledge

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403 Personalisation of SOA Registry Query Results: Implementation, Performance Analysis and Scalability Evaluation

Authors: Kee-Leong Tan, Karyn Wei-Ju Khoo, Hui-Na Chua

Abstract:

Service discovery is a very important component of Service Oriented Architectures (SOA). This paper presents two alternative approaches to customise the query results of private service registry such as Universal Description, Discovery and Integration (UDDI). The customisation is performed based on some pre-defined and/or real-time changing parameters. This work identifies the requirements, designs and additional mechanisms that must be applied to UDDI in order to support this customisation capability. We also detail the implements of the approaches and examine its performance and scalability. Based on our experimental results, we conclude that both approaches can be used to customise registry query results, but by storing personalization parameters in external resource will yield better performance and but less scalable when size of query results increases. We believe these approaches when combined with semantics enabled service registry will enhance the service discovery methods within a private UDDI registry environment.

Keywords: Service Oriented Architecture (SOA), Web service, Service discovery, registry, UDDI

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402 Re-Optimization MVPP Using Common Subexpression for Materialized View Selection

Authors: Boontita Suchyukorn, Raweewan Auepanwiriyakul

Abstract:

A Data Warehouses is a repository of information integrated from source data. Information stored in data warehouse is the form of materialized in order to provide the better performance for answering the queries. Deciding which appropriated views to be materialized is one of important problem. In order to achieve this requirement, the constructing search space close to optimal is a necessary task. It will provide effective result for selecting view to be materialized. In this paper we have proposed an approach to reoptimize Multiple View Processing Plan (MVPP) by using global common subexpressions. The merged queries which have query processing cost not close to optimal would be rewritten. The experiment shows that our approach can help to improve the total query processing cost of MVPP and sum of query processing cost and materialized view maintenance cost is reduced as well after views are selected to be materialized.

Keywords: Data Warehouse, materialized views, query rewriting, common subexpressions.

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401 A Study about the Distribution of the Spanning Ratios of Yao Graphs

Authors: Maryam Hsaini, Mostafa Nouri-Baygi

Abstract:

A critical problem in wireless sensor networks is limited battery and memory of nodes. Therefore, each node in the network could maintain only a subset of its neighbors to communicate with. This will increase the battery usage in the network because each packet should take more hops to reach its destination. In order to tackle these problems, spanner graphs are defined. Since each node has a small degree in a spanner graph and the distance in the graph is not much greater than its actual geographical distance, spanner graphs are suitable candidates to be used for the topology of a wireless sensor network. In this paper, we study Yao graphs and their behavior for a randomly selected set of points. We generate several random point sets and compare the properties of their Yao graphs with the complete graph. Based on our data sets, we obtain several charts demonstrating how Yao graphs behave for a set of randomly chosen point set. As the results show, the stretch factor of a Yao graph follows a normal distribution. Furthermore, the stretch factor is in average far less than the worst case stretch factor proved for Yao graphs in previous results. Furthermore, we use Yao graph for a realistic point set and study its stretch factor in real world.

Keywords: Wireless sensor network, spanner graph, Yao Graph.

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400 Visualization of Code Clone Detection Results and the Implementation with Structured Data

Authors: Kazuaki Maeda

Abstract:

This paper describes a code clone visualization method, called FC graph, and the implementation issues. Code clone detection tools usually show the results in a textual representation. If the results are large, it makes a problem to software maintainers with understanding them. One of the approaches to overcome the situation is visualization of code clone detection results. A scatter plot is a popular approach to the visualization. However, it represents only one-to-one correspondence and it is difficult to find correspondence of code clones over multiple files. FC graph represents correspondence among files, code clones and packages in Java. All nodes in FC graph are positioned using force-directed graph layout, which is dynami- cally calculated to adjust the distances of nodes until stabilizing them. We applied FC graph to some open source programs and visualized the results. In the author’s experience, FC graph is helpful to grasp correspondence of code clones over multiple files and also code clones with in a file.

Keywords: code clone detection, program comprehension, software maintenance, visualization

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399 The Giant Component in a Random Subgraph of a Weak Expander

Authors: Yilun Shang

Abstract:

In this paper, we investigate the appearance of the giant component in random subgraphs G(p) of a given large finite graph family Gn = (Vn, En) in which each edge is present independently with probability p. We show that if the graph Gn satisfies a weak isoperimetric inequality and has bounded degree, then the probability p under which G(p) has a giant component of linear order with some constant probability is bounded away from zero and one. In addition, we prove the probability of abnormally large order of the giant component decays exponentially. When a contact graph is modeled as Gn, our result is of special interest in the study of the spread of infectious diseases or the identification of community in various social networks.

Keywords: subgraph, expander, random graph, giant component, percolation.

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398 Information Retrieval in the Semantic LIFE Personal Digital Memory Framework

Authors: Hanh Huu Hoang, Tho Manh Nguyen

Abstract:

Ever increasing capacities of contemporary storage devices inspire the vision to accumulate (personal) information without the need of deleting old data over a long time-span. Hence the target of SemanticLIFE project is to create a Personal Information Management system for a human lifetime data. One of the most important characteristics of the system is its dedication to retrieve information in a very efficient way. By adopting user demands regarding the reduction of ambiguities, our approach aims at a user-oriented and yet powerful enough system with a satisfactory query performance. We introduce the query system of SemanticLIFE, the Virtual Query System, which uses emerging Semantic Web technologies to fulfill users- requirements.

Keywords: Ontology-based Information Retrieval, Digital Memories, SemanticLIFE.

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397 Electrical and Magnetic Modelling of a Power Transformer: A Bond Graph Approach

Authors: Gilberto Gonzalez-A, Dunia Nuñez-P

Abstract:

Bond graph models of an electrical transformer including the nonlinear saturation are presented. The transformer using electrical and magnetic circuits are modelled. These models determine the relation between self and mutual inductances, and the leakage and magnetizing inductances of power transformers with two windings using the properties of a bond graph. The equivalence between electrical and magnetic variables is given. The modelling and analysis using this methodology to three phase power transformers can be extended.

Keywords: Bond graph, electrical transformer, magnetic circuits, nonlinear saturation.

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396 Ontology-based Query System for UNITEN Postgraduate Students

Authors: Zaihisma C. Cob, Alicia Y.C. Tang, Sharifah J. Syed Aziz

Abstract:

This paper proposes a new model to support user queries on postgraduate research information at Universiti Tenaga Nasional. The ontology to be developed will contribute towards shareable and reusable domain knowledge that makes knowledge assets intelligently accessible to both people and software. This work adapts a methodology for ontology development based on the framework proposed by Uschold and King. The concepts and relations in this domain are represented in a class diagram using the Protégé software. The ontology will be used to support a menudriven query system for assisting students in searching for information related to postgraduate research at the university.

Keywords: Ontology, Protégé, postgraduate program, query system.

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395 Another Formal Proposal For Stealth

Authors: Adrien Derock, Pascal Veron

Abstract:

Taking into account the link between the efficiency of a detector and the complexity of a stealth mechanism, we propose in this paper a new formalism for stealth using graph theory.

Keywords: Detection, eradication, graph, rootkit, stealth.

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394 Distributed 2-Vertex Connectivity Test of Graphs Using Local Knowledge

Authors: Brahim Hamid, Bertrand Le Saec, Mohamed Mosbah

Abstract:

The vertex connectivity of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. This work is devoted to the problem of vertex connectivity test of graphs in a distributed environment based on a general and a constructive approach. The contribution of this paper is threefold. First, using a preconstructed spanning tree of the considered graph, we present a protocol to test whether a given graph is 2-connected using only local knowledge. Second, we present an encoding of this protocol using graph relabeling systems. The last contribution is the implementation of this protocol in the message passing model. For a given graph G, where M is the number of its edges, N the number of its nodes and Δ is its degree, our algorithms need the following requirements: The first one uses O(Δ×N2) steps and O(Δ×logΔ) bits per node. The second one uses O(Δ×N2) messages, O(N2) time and O(Δ × logΔ) bits per node. Furthermore, the studied network is semi-anonymous: Only the root of the pre-constructed spanning tree needs to be identified.

Keywords: Distributed computing, fault-tolerance, graph relabeling systems, local computations, local knowledge, message passing system, networks, vertex connectivity.

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393 Courses Pre-Required Visualization Using Force Directed Placement Technique

Authors: Imen Ammari, Mourad Elloumi, Ala Eddine Barouni

Abstract:

Visualizing “Courses – Pre – Required - Architecture" on the screen has proven to be useful and helpful for university actors and specially for students. In fact, these students can easily identify courses and their pre required, perceive the courses to follow in the future, and then can choose rapidly the appropriate course to register in. Given a set of courses and their prerequired, we present an algorithm for visualization a graph entitled “Courses-Pre-Required-Graph" that present courses and their prerequired in order to help students to recognize, lonely, what courses to take in the future and perceive the contain of all courses that they will study. Our algorithm using “Force Directed Placement" technique visualizes the “Courses-Pre-Required-Graph" in such way that courses are easily identifiable. The time complexity of our drawing algorithm is O (n2), where n is the number of courses in the “Courses-Pre-Required-Graph".

Keywords: Courses–Pre-Required-Architecture, Courses-Pre- Required-Graph, Courses-Pre-Required-Visualization, Force directed Placement, Resolution.

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392 Performance Analysis of Learning Automata-Based Routing Algorithms in Sparse Graphs

Authors: Z.Farhadpour, Mohammad.R.Meybodi

Abstract:

A number of routing algorithms based on learning automata technique have been proposed for communication networks. How ever, there has been little work on the effects of variation of graph scarcity on the performance of these algorithms. In this paper, a comprehensive study is launched to investigate the performance of LASPA, the first learning automata based solution to the dynamic shortest path routing, across different graph structures with varying scarcities. The sensitivity of three main performance parameters of the algorithm, being average number of processed nodes, scanned edges and average time per update, to variation in graph scarcity is reported. Simulation results indicate that the LASPA algorithm can adapt well to the scarcity variation in graph structure and gives much better outputs than the existing dynamic and fixed algorithms in terms of performance criteria.

Keywords: Learning automata, routing, algorithm, sparse graph

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391 AI Tutor: A Computer Science Domain Knowledge Graph-Based QA System on JADE platform

Authors: Yingqi Cui, Changran Huang, Raymond Lee

Abstract:

In this paper, we proposed an AI Tutor using ontology and natural language process techniques to generate a computer science domain knowledge graph and answer users’ questions based on the knowledge graph. We define eight types of relation to extract relationships between entities according to the computer science domain text. The AI tutor is separated into two agents: learning agent and Question-Answer (QA) agent and developed on JADE (a multi-agent system) platform. The learning agent is responsible for reading text to extract information and generate a corresponding knowledge graph by defined patterns. The QA agent can understand the users’ questions and answer humans’ questions based on the knowledge graph generated by the learning agent.

Keywords: Artificial intelligence, natural language process, knowledge graph, agent, QA system.

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390 Complexity Analysis of Some Known Graph Coloring Instances

Authors: Jeffrey L. Duffany

Abstract:

Graph coloring is an important problem in computer science and many algorithms are known for obtaining reasonably good solutions in polynomial time. One method of comparing different algorithms is to test them on a set of standard graphs where the optimal solution is already known. This investigation analyzes a set of 50 well known graph coloring instances according to a set of complexity measures. These instances come from a variety of sources some representing actual applications of graph coloring (register allocation) and others (mycieleski and leighton graphs) that are theoretically designed to be difficult to solve. The size of the graphs ranged from ranged from a low of 11 variables to a high of 864 variables. The method used to solve the coloring problem was the square of the adjacency (i.e., correlation) matrix. The results show that the most difficult graphs to solve were the leighton and the queen graphs. Complexity measures such as density, mobility, deviation from uniform color class size and number of block diagonal zeros are calculated for each graph. The results showed that the most difficult problems have low mobility (in the range of .2-.5) and relatively little deviation from uniform color class size.

Keywords: graph coloring, complexity, algorithm.

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389 Analyzing the Factors that Cause Parallel Performance Degradation in Parallel Graph-Based Computations Using Graph500

Authors: Mustafa Elfituri, Jonathan Cook

Abstract:

Recently, graph-based computations have become more important in large-scale scientific computing as they can provide a methodology to model many types of relations between independent objects. They are being actively used in fields as varied as biology, social networks, cybersecurity, and computer networks. At the same time, graph problems have some properties such as irregularity and poor locality that make their performance different than regular applications performance. Therefore, parallelizing graph algorithms is a hard and challenging task. Initial evidence is that standard computer architectures do not perform very well on graph algorithms. Little is known exactly what causes this. The Graph500 benchmark is a representative application for parallel graph-based computations, which have highly irregular data access and are driven more by traversing connected data than by computation. In this paper, we present results from analyzing the performance of various example implementations of Graph500, including a shared memory (OpenMP) version, a distributed (MPI) version, and a hybrid version. We measured and analyzed all the factors that affect its performance in order to identify possible changes that would improve its performance. Results are discussed in relation to what factors contribute to performance degradation.

Keywords: Graph computation, Graph500 benchmark, parallel architectures, parallel programming, workload characterization.

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388 A Hybrid Ontology Based Approach for Ranking Documents

Authors: Sarah Motiee, Azadeh Nematzadeh, Mehrnoush Shamsfard

Abstract:

Increasing growth of information volume in the internet causes an increasing need to develop new (semi)automatic methods for retrieval of documents and ranking them according to their relevance to the user query. In this paper, after a brief review on ranking models, a new ontology based approach for ranking HTML documents is proposed and evaluated in various circumstances. Our approach is a combination of conceptual, statistical and linguistic methods. This combination reserves the precision of ranking without loosing the speed. Our approach exploits natural language processing techniques to extract phrases from documents and the query and doing stemming on words. Then an ontology based conceptual method will be used to annotate documents and expand the query. To expand a query the spread activation algorithm is improved so that the expansion can be done flexible and in various aspects. The annotated documents and the expanded query will be processed to compute the relevance degree exploiting statistical methods. The outstanding features of our approach are (1) combining conceptual, statistical and linguistic features of documents, (2) expanding the query with its related concepts before comparing to documents, (3) extracting and using both words and phrases to compute relevance degree, (4) improving the spread activation algorithm to do the expansion based on weighted combination of different conceptual relationships and (5) allowing variable document vector dimensions. A ranking system called ORank is developed to implement and test the proposed model. The test results will be included at the end of the paper.

Keywords: Document ranking, Ontology, Spread activation algorithm, Annotation.

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387 Approximating Maximum Weighted Independent Set Using Vertex Support

Authors: S. Balaji, V. Swaminathan, K. Kannan

Abstract:

The Maximum Weighted Independent Set (MWIS) problem is a classic graph optimization NP-hard problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the MWIS problem is to find a vertex set S V whose total weight is maximum subject to no two vertices in S are adjacent. This paper presents a novel approach to approximate the MWIS of a graph using minimum weighted vertex cover of the graph. Computational experiments are designed and conducted to study the performance of our proposed algorithm. Extensive simulation results show that the proposed algorithm can yield better solutions than other existing algorithms found in the literature for solving the MWIS.

Keywords: weighted independent set, vertex cover, vertex support, heuristic, NP - hard problem.

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386 Face Recognition using a Kernelization of Graph Embedding

Authors: Pang Ying Han, Hiew Fu San, Ooi Shih Yin

Abstract:

Linearization of graph embedding has been emerged as an effective dimensionality reduction technique in pattern recognition. However, it may not be optimal for nonlinearly distributed real world data, such as face, due to its linear nature. So, a kernelization of graph embedding is proposed as a dimensionality reduction technique in face recognition. In order to further boost the recognition capability of the proposed technique, the Fisher-s criterion is opted in the objective function for better data discrimination. The proposed technique is able to characterize the underlying intra-class structure as well as the inter-class separability. Experimental results on FRGC database validate the effectiveness of the proposed technique as a feature descriptor.

Keywords: Face recognition, Fisher discriminant, graph embedding, kernelization.

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385 Phasor Analysis of a Synchronous Generator: A Bond Graph Approach

Authors: Israel Núñez-Hernández, Peter C. Breedveld, Paul B. T. Weustink, Gilberto Gonzalez-A

Abstract:

This paper presents the use of phasor bond graphs to obtain the steady-state behavior of a synchronous generator. The phasor bond graph elements are built using 2D multibonds, which represent the real and imaginary part of the phasor. The dynamic bond graph model of a salient-pole synchronous generator is showed, and verified viz. a sudden short-circuit test. The reduction of the dynamic model into a phasor representation is described. The previous test is executed on the phasor bond graph model, and its steady-state values are compared with the dynamic response. Besides, the widely used power (torque)-angle curves are obtained by means of the phasor bond graph model, to test the usefulness of this model.

Keywords: Bond graphs, complex power, phasors, synchronous generator, short-circuit, open-circuit, power-angle curve.

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384 N-Sun Decomposition of Complete Graphs and Complete Bipartite Graphs

Authors: R. Anitha, R. S. Lekshmi

Abstract:

Graph decompositions are vital in the study of combinatorial design theory. Given two graphs G and H, an H-decomposition of G is a partition of the edge set of G into disjoint isomorphic copies of H. An n-sun is a cycle Cn with an edge terminating in a vertex of degree one attached to each vertex. In this paper we have proved that the complete graph of order 2n, K2n can be decomposed into n-2 n-suns, a Hamilton cycle and a perfect matching, when n is even and for odd case, the decomposition is n-1 n-suns and a perfect matching. For an odd order complete graph K2n+1, delete the star subgraph K1, 2n and the resultant graph K2n is decomposed as in the case of even order. The method of building n-suns uses Walecki's construction for the Hamilton decomposition of complete graphs. A spanning tree decomposition of even order complete graphs is also discussed using the labeling scheme of n-sun decomposition. A complete bipartite graph Kn, n can be decomposed into n/2 n-suns when n/2 is even. When n/2 is odd, Kn, n can be decomposed into (n-2)/2 n-suns and a Hamilton cycle.

Keywords: Hamilton cycle, n-sun decomposition, perfectmatching, spanning tree.

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