Search results for: Graph Partition
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 378

Search results for: Graph Partition

138 Distributed Data-Mining by Probability-Based Patterns

Authors: M. Kargar, F. Gharbalchi

Abstract:

In this paper a new method is suggested for distributed data-mining by the probability patterns. These patterns use decision trees and decision graphs. The patterns are cared to be valid, novel, useful, and understandable. Considering a set of functions, the system reaches to a good pattern or better objectives. By using the suggested method we will be able to extract the useful information from massive and multi-relational data bases.

Keywords: Data-mining, Decision tree, Decision graph, Pattern, Relationship.

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137 Research on the Transformation of Bottom Space in the Teaching Area of Zijingang Campus, Zhejiang University

Authors: Jia Xu

Abstract:

There is a lot of bottom space in the teaching area of Zijingang Campus of Zhejiang University, which benefits to the ventilation, heat dissipation, circulation, partition of quiet and noisy areas and diversification of spaces. Hangzhou is hot in summer but cold in winter, so teachers and students spend much less time in the bottom space of buildings in winter than in summer. Recently, depending on the teachers and students’ proposals, the school transformed the bottom space in the teaching area to provide space for relaxing, chatting and staying in winter. Surveying and analyzing the existing ways to transform, the paper researches deeply on the transformation projects of bottom space in the teaching buildings. It is believed that this paper can be a salutary lesson to make the bottom space in the teaching areas of universities richer and bring more diverse activities for teachers and students.

Keywords: Bottom space, teaching area, transformation, Zijingang Campus of Zhejiang University.

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136 Quantum Statistical Mechanical Formulations of Three-Body Problems via Non-Local Potentials

Authors: A. Maghari, V. H. Maleki

Abstract:

In this paper, we present a quantum statistical mechanical formulation from our recently analytical expressions for partial-wave transition matrix of a three-particle system. We report the quantum reactive cross sections for three-body scattering processes 1+(2,3)→1+(2,3) as well as recombination 1+(2,3)→1+(3,1) between one atom and a weakly-bound dimer. The analytical expressions of three-particle transition matrices and their corresponding cross-sections were obtained from the threedimensional Faddeev equations subjected to the rank-two non-local separable potentials of the generalized Yamaguchi form. The equilibrium quantum statistical mechanical properties such partition function and equation of state as well as non-equilibrium quantum statistical properties such as transport cross-sections and their corresponding transport collision integrals were formulated analytically. This leads to obtain the transport properties, such as viscosity and diffusion coefficient of a moderate dense gas.

Keywords: Statistical mechanics, Nonlocal separable potential, three-body interaction, Faddeev equations.

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135 Novel Anti-leukemia Calanone Compounds by Quantitative Structure-Activity Relationship AM1 Semiempirical Method

Authors: Ponco Iswanto, Mochammad Chasani, Muhammad Hanafi, Iqmal Tahir, Eva Vaulina YD, Harjono, Lestari Solikhati, Winkanda S. Putra, Yayuk Yuliantini

Abstract:

Quantitative Structure-Activity Relationship (QSAR) approach for discovering novel more active Calanone derivative as anti-leukemia compound has been conducted. There are 6 experimental activities of Calanone compounds against leukemia cell L1210 that are used as material of the research. Calculation of theoretical predictors (independent variables) was performed by AM1 semiempirical method. The QSAR equation is determined by Principle Component Regression (PCR) analysis, with Log IC50 as dependent variable and the independent variables are atomic net charges, dipole moment (μ), and coefficient partition of noctanol/ water (Log P). Three novel Calanone derivatives that obtained by this research have higher activity against leukemia cell L1210 than pure Calanone.

Keywords: AM1 semiempirical calculation, Calanone, Principle Component Regression, QSAR approach.

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134 Minimizing Mutant Sets by Equivalence and Subsumption

Authors: Samia Alblwi, Amani Ayad

Abstract:

Mutation testing is the art of generating syntactic variations of a base program and checking whether a candidate test suite can identify all the mutants that are not semantically equivalent to the base; this technique can be used to assess the quality of test suite. One of the main obstacles to the widespread use of mutation testing is cost, as even small programs (a few dozen lines of code) can give rise to a large number of mutants (up to hundreds); this has created an incentive to seek to reduce the number of mutants while preserving their collective effectiveness. Two criteria have been used to reduce the size of mutant sets: equivalence, which aims to partition the set of mutants into equivalence classes modulo semantic equivalence, and selecting one representative per class; and, subsumption, which aims to define a partial ordering among mutants that ranks mutants by effectiveness and seeks to select maximal elements in this ordering. In this paper, we analyze these two policies using analytical and empirical criteria.

Keywords: Mutation testing, mutant sets, mutant equivalence, mutant subsumption, mutant set minimization.

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133 Face Texture Reconstruction for Illumination Variant Face Recognition

Authors: Pengfei Xiong, Lei Huang, Changping Liu

Abstract:

In illumination variant face recognition, existing methods extracting face albedo as light normalized image may lead to loss of extensive facial details, with light template discarded. To improve that, a novel approach for realistic facial texture reconstruction by combining original image and albedo image is proposed. First, light subspaces of different identities are established from the given reference face images; then by projecting the original and albedo image into each light subspace respectively, texture reference images with corresponding lighting are reconstructed and two texture subspaces are formed. According to the projections in texture subspaces, facial texture with normal light can be synthesized. Due to the combination of original image, facial details can be preserved with face albedo. In addition, image partition is applied to improve the synthesization performance. Experiments on Yale B and CMUPIE databases demonstrate that this algorithm outperforms the others both in image representation and in face recognition.

Keywords: texture reconstruction, illumination, face recognition, subspaces

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132 Real-Time Vision-based Korean Finger Spelling Recognition System

Authors: Anjin Park, Sungju Yun, Jungwhan Kim, Seungk Min, Keechul Jung

Abstract:

Finger spelling is an art of communicating by signs made with fingers, and has been introduced into sign language to serve as a bridge between the sign language and the verbal language. Previous approaches to finger spelling recognition are classified into two categories: glove-based and vision-based approaches. The glove-based approach is simpler and more accurate recognizing work of hand posture than vision-based, yet the interfaces require the user to wear a cumbersome and carry a load of cables that connected the device to a computer. In contrast, the vision-based approaches provide an attractive alternative to the cumbersome interface, and promise more natural and unobtrusive human-computer interaction. The vision-based approaches generally consist of two steps: hand extraction and recognition, and two steps are processed independently. This paper proposes real-time vision-based Korean finger spelling recognition system by integrating hand extraction into recognition. First, we tentatively detect a hand region using CAMShift algorithm. Then fill factor and aspect ratio estimated by width and height estimated by CAMShift are used to choose candidate from database, which can reduce the number of matching in recognition step. To recognize the finger spelling, we use DTW(dynamic time warping) based on modified chain codes, to be robust to scale and orientation variations. In this procedure, since accurate hand regions, without holes and noises, should be extracted to improve the precision, we use graph cuts algorithm that globally minimize the energy function elegantly expressed by Markov random fields (MRFs). In the experiments, the computational times are less than 130ms, and the times are not related to the number of templates of finger spellings in database, as candidate templates are selected in extraction step.

Keywords: CAMShift, DTW, Graph Cuts, MRF.

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131 An Analysis of the Social Network Structure of Knowledge Management Students at NTU

Authors: Guo Yanru, Zhu Xiaobo, Lee Chu Keong

Abstract:

This paper maps the structure of the social network of the 2011 class ofsixty graduate students of the Masters of Science (Knowledge Management) programme at the Nanyang Technological University, based on their friending relationships on Facebook. To ensure anonymity, actual names were not used. Instead, they were replaced with codes constructed from their gender, nationality, mode of study, year of enrollment and a unique number. The relationships between friends within the class, and among the seniors and alumni of the programme wereplotted. UCINet and Pajek were used to plot the sociogram, to compute the density, inclusivity, and degree, global, betweenness, and Bonacich centralities, to partition the students into two groups, namely, active and peripheral, and to identify the cut-points. Homophily was investigated, and it was observed for nationality and study mode. The groups students formed on Facebook were also studied, and of fifteen groups, eight were classified as dead, which we defined as those that have been inactive for over two months.

Keywords: Facebook, friending relationships, Social network analysis, social network sites, structural position

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130 Optimal Path Planner for Autonomous Vehicles

Authors: M. Imran Akram, Ahmed Pasha, Nabeel Iqbal

Abstract:

In this paper a real-time trajectory generation algorithm for computing 2-D optimal paths for autonomous aerial vehicles has been discussed. A dynamic programming approach is adopted to compute k-best paths by minimizing a cost function. Collision detection is implemented to detect intersection of the paths with obstacles. Our contribution is a novel approach to the problem of trajectory generation that is computationally efficient and offers considerable gain over existing techniques.

Keywords: dynamic programming, graph search, path planning.

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129 Analysis of Social Network Using Clever Ant Colony Metaphor

Authors: Mohammad Al-Fayoumi, Soumya Banerjee, Jr., P. K. Mahanti

Abstract:

A social network is a set of people or organization or other social entities connected by some form of relationships. Analysis of social network broadly elaborates visual and mathematical representation of that relationship. Web can also be considered as a social network. This paper presents an innovative approach to analyze a social network using a variant of existing ant colony optimization algorithm called as Clever Ant Colony Metaphor. Experiments are performed and interesting findings and observations have been inferred based on the proposed model.

Keywords: Social Network, Ant Colony, Maximum Clique, Sub graph, Clever Ant colony.

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128 Optimum Performance Measures of Interdependent Queuing System with Controllable Arrival Rates

Authors: S. S. Mishra

Abstract:

In this paper, an attempt is made to compute the total optimal cost of interdependent queuing system with controllable arrival rates as an important performance measure of the system. An example of application has also been presented to exhibit the use of the model. Finally, numerical demonstration based on a computing algorithm and variational effects of the model with the help of the graph have also been presented.

Keywords: Computing, Controllable arrival rate, Optimum performance measure.

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127 Block Sorting: A New Characterization and a New Heuristic

Authors: Swapnoneel Roy, Ashok Kumar Thakur, Minhazur Rahman

Abstract:

The Block Sorting problem is to sort a given permutation moving blocks. A block is defined as a substring of the given permutation, which is also a substring of the identity permutation. Block Sorting has been proved to be NP-Hard. Until now two different 2-Approximation algorithms have been presented for block sorting. These are the best known algorithms for Block Sorting till date. In this work we present a different characterization of Block Sorting in terms of a transposition cycle graph. Then we suggest a heuristic, which we show to exhibit a 2-approximation performance guarantee for most permutations.

Keywords: Block Sorting, Optical Character Recognition, Genome Rearrangements, Sorting Primitives, ApproximationAlgorithms

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126 A Finite-Time Consensus Protocol of the Multi-Agent Systems

Authors: Xin-Lei Feng, Ting-Zhu Huang

Abstract:

According to conjugate gradient algorithm, a new consensus protocol algorithm of discrete-time multi-agent systems is presented, which can achieve finite-time consensus. Finally, a numerical example is given to illustrate our theoretical result.

Keywords: Consensus protocols; Graph theory; Multi-agent systems;Conjugate gradient algorithm; Finite-time.

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125 Tool for Fast Detection of Java Code Snippets

Authors: Tomáš Bublík, Miroslav Virius

Abstract:

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.

Keywords: AST, Java, tree matching, Scripthon, source code recognition

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124 A Reconfigurable Distributed Multiagent System Optimized for Scalability

Authors: Summiya Moheuddin, Afzel Noore, Muhammad Choudhry

Abstract:

This paper proposes a novel solution for optimizing the size and communication overhead of a distributed multiagent system without compromising the performance. The proposed approach addresses the challenges of scalability especially when the multiagent system is large. A modified spectral clustering technique is used to partition a large network into logically related clusters. Agents are assigned to monitor dedicated clusters rather than monitor each device or node. The proposed scalable multiagent system is implemented using JADE (Java Agent Development Environment) for a large power system. The performance of the proposed topologyindependent decentralized multiagent system and the scalable multiagent system is compared by comprehensively simulating different fault scenarios. The time taken for reconfiguration, the overall computational complexity, and the communication overhead incurred are computed. The results of these simulations show that the proposed scalable multiagent system uses fewer agents efficiently, makes faster decisions to reconfigure when a fault occurs, and incurs significantly less communication overhead.

Keywords: Multiagent system, scalable design, spectral clustering, reconfiguration.

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123 Covering-based Rough sets Based on the Refinement of Covering-element

Authors: Jianguo Tang, Kun She, William Zhu

Abstract:

Covering-based rough sets is an extension of rough sets and it is based on a covering instead of a partition of the universe. Therefore it is more powerful in describing some practical problems than rough sets. However, by extending the rough sets, covering-based rough sets can increase the roughness of each model in recognizing objects. How to obtain better approximations from the models of a covering-based rough sets is an important issue. In this paper, two concepts, determinate elements and indeterminate elements in a universe, are proposed and given precise definitions respectively. This research makes a reasonable refinement of the covering-element from a new viewpoint. And the refinement may generate better approximations of covering-based rough sets models. To prove the theory above, it is applied to eight major coveringbased rough sets models which are adapted from other literature. The result is, in all these models, the lower approximation increases effectively. Correspondingly, in all models, the upper approximation decreases with exceptions of two models in some special situations. Therefore, the roughness of recognizing objects is reduced. This research provides a new approach to the study and application of covering-based rough sets.

Keywords: Determinate element, indeterminate element, refinementof covering-element, refinement of covering, covering-basedrough sets.

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122 Face Recognition: A Literature Review

Authors: A. S. Tolba, A.H. El-Baz, A.A. El-Harby

Abstract:

The task of face recognition has been actively researched in recent years. This paper provides an up-to-date review of major human face recognition research. We first present an overview of face recognition and its applications. Then, a literature review of the most recent face recognition techniques is presented. Description and limitations of face databases which are used to test the performance of these face recognition algorithms are given. A brief summary of the face recognition vendor test (FRVT) 2002, a large scale evaluation of automatic face recognition technology, and its conclusions are also given. Finally, we give a summary of the research results.

Keywords: Combined classifiers, face recognition, graph matching, neural networks.

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121 Knowledge Based Chords Manipulation in MES

Authors: V. Hepsiba Mabel, K. Alagarsamy, Justus S.

Abstract:

Chord formation in western music notations is an intelligent art form which is learnt over the years by a musician to acquire it. Still it is a question of creativity that brings the perfect chord sequence that matches music score. This work focuses on the process of forming chords using a custom-designed knowledgebase (KB) of Music Expert System. An optimal Chord-Set for a given music score is arrived by using the chord-pool in the KB and the finding the chord match using Jusic Distance (JD). Conceptual Graph based knowledge representation model is followed for knowledge storage and retrieval in the knowledgebase.

Keywords: Knowledge, Music, Representation, Knowledgebase, Chord-Set.

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120 Fuzzy Shortest Paths Approximation for Solving the Fuzzy Steiner Tree Problem in Graphs

Authors: Miloš Šeda

Abstract:

In this paper, we deal with the Steiner tree problem (STP) on a graph in which a fuzzy number, instead of a real number, is assigned to each edge. We propose a modification of the shortest paths approximation based on the fuzzy shortest paths (FSP) evaluations. Since a fuzzy min operation using the extension principle leads to nondominated solutions, we propose another approach to solving the FSP using Cheng's centroid point fuzzy ranking method.

Keywords: Steiner tree, single shortest path problem, fuzzyranking, binary heap, priority queue.

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119 Modeling Approaches for Large-Scale Reconfigurable Engineering Systems

Authors: Kwa-Sur Tam

Abstract:

This paper reviews various approaches that have been used for the modeling and simulation of large-scale engineering systems and determines their appropriateness in the development of a RICS modeling and simulation tool. Bond graphs, linear graphs, block diagrams, differential and difference equations, modeling languages, cellular automata and agents are reviewed. This tool should be based on linear graph representation and supports symbolic programming, functional programming, the development of noncausal models and the incorporation of decentralized approaches.

Keywords: Interdisciplinary, dynamic, functional programming, object-oriented.

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118 On Strong(Weak) Domination in Fuzzy Graphs

Authors: C.Natarajan, S.K.Ayyaswamy

Abstract:

Let G be a fuzzy graph. Then D Ôèå V is said to be a strong (weak) fuzzy dominating set of G if every vertex v ∈ V -D is strongly (weakly) dominated by some vertex u in D. We denote a strong (weak) fuzzy dominating set by sfd-set (wfd-set). The minimum scalar cardinality of a sfd-set (wfd-set) is called the strong (weak) fuzzy domination number of G and it is denoted by γsf (G)γwf (G). In this paper we introduce the concept of strong (weak) domination in fuzzy graphs and obtain some interesting results for this new parameter in fuzzy graphs.

Keywords: Fuzzy graphs, fuzzy domination, strong (weak) fuzzy domination number.

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117 Mutually Independent Hamiltonian Cycles of Cn x Cn

Authors: Kai-Siou Wu, Justie Su-Tzu Juan

Abstract:

In a graph G, a cycle is Hamiltonian cycle if it contain all vertices of G. Two Hamiltonian cycles C_1 = ⟨u_0, u_1, u_2, ..., u_{n−1}, u_0⟩ and C_2 = ⟨v_0, v_1, v_2, ..., v_{n−1}, v_0⟩ in G are independent if u_0 = v_0, u_i = ̸ v_i for all 1 ≤ i ≤ n−1. In G, a set of Hamiltonian cycles C = {C_1, C_2, ..., C_k} is mutually independent if any two Hamiltonian cycles of C are independent. The mutually independent Hamiltonicity IHC(G), = k means there exist a maximum integer k such that there exists k-mutually independent Hamiltonian cycles start from any vertex of G. In this paper, we prove that IHC(C_n × C_n) = 4, for n ≥ 3.

Keywords: Hamiltonian, independent, cycle, Cartesian product, mutually independent Hamiltonicity

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116 On Minimum Cycle Bases of the Wreath Product of Wheels with Stars

Authors: M. M. M. Jaradat, M. K. Al-Qeyyam

Abstract:

The length of a cycle basis of a graph is the sum of the lengths of its elements. A minimum cycle basis is a cycle basis with minimum length. In this work, a construction of a minimum cycle basis for the wreath product of wheels with stars is presented. Moreover, the length of minimum cycle basis and the length of its longest cycle are calculated.

Keywords: Cycle space, minimum cycle basis, wreath product.

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115 SIPINA Induction Graph Method for Seismic Risk Prediction

Authors: B. Selma

Abstract:

The aim of this study is to test the feasibility of SIPINA method to predict the harmfulness parameters controlling the seismic response. The approach developed takes into consideration both the focal depth and the peak ground acceleration. The parameter to determine is displacement. The data used for the learning of this method and analysis nonlinear seismic are described and applied to a class of models damaged to some typical structures of the existing urban infrastructure of Jassy, Romania. The results obtained indicate an influence of the focal depth and the peak ground acceleration on the displacement.

Keywords: SIPINA method, seism, focal depth, peak ground acceleration, displacement.

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114 Effect of Interior Brick-infill Partitions on the Progressive Collapse Potential of a RC Building: Linear Static Analysis Results

Authors: Meng-Hao Tsai, Tsuei-Chiang Huang

Abstract:

Interior brick-infill partitions are usually considered as non-structural components, and only their weight is accounted for in practical structural design. In this study, the brick-infill panels are simulated by compression struts to clarify their effect on the progressive collapse potential of an earthquake-resistant RC building. Three-dimensional finite element models are constructed for the RC building subjected to sudden column loss. Linear static analyses are conducted to investigate the variation of demand-to-capacity ratio (DCR) of beam-end moment and the axial force variation of the beams adjacent to the removed column. Study results indicate that the brick-infill effect depends on their location with respect to the removed column. As they are filled in a structural bay with a shorter span adjacent to the column-removed line, more significant reduction of DCR may be achieved. However, under certain conditions, the brick infill may increase the axial tension of the two-span beam bridging the removed column.

Keywords: Progressive collapse, brick-infill partition, compression strut.

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113 A Comprehensive Review on Different Mixed Data Clustering Ensemble Methods

Authors: S. Sarumathi, N. Shanthi, S. Vidhya, M. Sharmila

Abstract:

An extensive amount of work has been done in data clustering research under the unsupervised learning technique in Data Mining during the past two decades. Moreover, several approaches and methods have been emerged focusing on clustering diverse data types, features of cluster models and similarity rates of clusters. However, none of the single clustering algorithm exemplifies its best nature in extracting efficient clusters. Consequently, in order to rectify this issue, a new challenging technique called Cluster Ensemble method was bloomed. This new approach tends to be the alternative method for the cluster analysis problem. The main objective of the Cluster Ensemble is to aggregate the diverse clustering solutions in such a way to attain accuracy and also to improve the eminence the individual clustering algorithms. Due to the massive and rapid development of new methods in the globe of data mining, it is highly mandatory to scrutinize a vital analysis of existing techniques and the future novelty. This paper shows the comparative analysis of different cluster ensemble methods along with their methodologies and salient features. Henceforth this unambiguous analysis will be very useful for the society of clustering experts and also helps in deciding the most appropriate one to resolve the problem in hand.

Keywords: Clustering, Cluster Ensemble Methods, Coassociation matrix, Consensus Function, Median Partition.

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112 Induced Acyclic Path Decomposition in Graphs

Authors: Abraham V. M., I. Sahul Hamid

Abstract:

A decomposition of a graph G is a collection ψ of graphs H1,H2, . . . , Hr of G such that every edge of G belongs to exactly one Hi. If each Hi is either an induced path in G, then ψ is called an induced acyclic path decomposition of G and if each Hi is a (induced) cycle in G then ψ is called a (induced) cycle decomposition of G. The minimum cardinality of an induced acyclic path decomposition of G is called the induced acyclic path decomposition number of G and is denoted by ¤Çia(G). Similarly the cyclic decomposition number ¤Çc(G) is defined. In this paper we begin an investigation of these parameters.

Keywords: Cycle decomposition, Induced acyclic path decomposition, Induced acyclic path decomposition number.

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111 Using Multi-Thread Technology Realize Most Short-Path Parallel Algorithm

Authors: Chang-le Lu, Yong Chen

Abstract:

The shortest path question is in a graph theory model question, and it is applied in many fields. The most short-path question may divide into two kinds: Single sources most short-path, all apexes to most short-path. This article mainly introduces the problem of all apexes to most short-path, and gives a new parallel algorithm of all apexes to most short-path according to the Dijkstra algorithm. At last this paper realizes the parallel algorithms in the technology of C # multithreading.

Keywords: Dijkstra algorithm, parallel algorithms, multi-thread technology, most short-path, ratio.

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110 Double Diffusive Convection in a Partially Porous Cavity under Suction/Injection Effects

Authors: Y. Outaleb, K. Bouhadef, O. Rahli

Abstract:

Double-diffusive steady convection in a partially porous cavity with partially permeable walls and under the combined buoyancy effects of thermal and mass diffusion was analysed numerically using finite volume method. The top wall is well insulated and impermeable while the bottom surface is partially well insulated and impermeable and partially submitted to constant temperature T1 and concentration C1. Constant equal temperature T2 and concentration C2 are imposed along the vertical surfaces of the enclosure. Mass suction/injection and injection/suction are respectively considered at the bottom of the porous centred partition and at one of the vertical walls. Heat and mass transfer characteristics as streamlines and average Nusselt numbers and Sherwood numbers were discussed for different values of buoyancy ratio, Rayleigh number, and injection/suction coefficient. It is especially noted that increasing the injection factor disadvantages the exchanges in the case of the injection while the transfer is augmented in case of suction. On the other hand, a critical value of the buoyancy ratio was highlighted for which heat and mass transfers are minimized.

Keywords: Double diffusive convection, Injection/Extraction, Partially porous cavity

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109 An Implementation of MacMahon's Partition Analysis in Ordering the Lower Bound of Processing Elements for the Algorithm of LU Decomposition

Authors: Halil Snopce, Ilir Spahiu, Lavdrim Elmazi

Abstract:

A lot of Scientific and Engineering problems require the solution of large systems of linear equations of the form bAx in an effective manner. LU-Decomposition offers good choices for solving this problem. Our approach is to find the lower bound of processing elements needed for this purpose. Here is used the so called Omega calculus, as a computational method for solving problems via their corresponding Diophantine relation. From the corresponding algorithm is formed a system of linear diophantine equalities using the domain of computation which is given by the set of lattice points inside the polyhedron. Then is run the Mathematica program DiophantineGF.m. This program calculates the generating function from which is possible to find the number of solutions to the system of Diophantine equalities, which in fact gives the lower bound for the number of processors needed for the corresponding algorithm. There is given a mathematical explanation of the problem as well. Keywordsgenerating function, lattice points in polyhedron, lower bound of processor elements, system of Diophantine equationsand : calculus.

Keywords: generating function, lattice points in polyhedron, lower bound of processor elements, system of Diophantine equations and calculus.

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