Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 11

graph Related Abstracts

11 An Optimized Association Rule Mining Algorithm

Authors: Jyoti Agarwal, Archana Singh, Ajay Rana


Data Mining is an efficient technology to discover patterns in large databases. Association Rule Mining techniques are used to find the correlation between the various item sets in a database, and this co-relation between various item sets are used in decision making and pattern analysis. In recent years, the problem of finding association rules from large datasets has been proposed by many researchers. Various research papers on association rule mining (ARM) are studied and analyzed first to understand the existing algorithms. Apriori algorithm is the basic ARM algorithm, but it requires so many database scans. In DIC algorithm, less amount of database scan is needed but complex data structure lattice is used. The main focus of this paper is to propose a new optimized algorithm (Friendly Algorithm) and compare its performance with the existing algorithms A data set is used to find out frequent itemsets and association rules with the help of existing and proposed (Friendly Algorithm) and it has been observed that the proposed algorithm also finds all the frequent itemsets and essential association rules from databases as compared to existing algorithms in less amount of database scan. In the proposed algorithm, an optimized data structure is used i.e. Graph and Adjacency Matrix.

Keywords: Data Mining, Association Rules, dynamic item set counting, FP-growth, friendly algorithm, graph

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10 A Graph SEIR Cellular Automata Based Model to Study the Spreading of a Transmittable Disease

Authors: Kulbhushan Agnihotri, Natasha Sharma


Cellular Automata are discrete dynamical systems which are based on local character and spatial disparateness of the spreading process. These factors are generally neglected by traditional models based on differential equations for epidemic spread. The aim of this work is to introduce an SEIR model based on cellular automata on graphs to imitate epidemic spreading. Distinctively, it is an SEIR-type model where the population is divided into susceptible, exposed, infected and recovered individuals. The results obtained from simulations are in accordance with the spreading behavior of a real time epidemics.

Keywords: epidemic spread, cellular automata, graph, susceptible

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9 The Second Smallest Eigenvalue of Complete Tripartite Hypergraph

Authors: M. Salman, Hanni Garminia, Alfi Y. Zakiyyah, A. N. Irawati


In the terminology of the hypergraph, there is a relation with the terminology graph. In the theory of graph, the edges connected two vertices. In otherwise, in hypergraph, the edges can connect more than two vertices. There is representation matrix of a graph such as adjacency matrix, Laplacian matrix, and incidence matrix. The adjacency matrix is symmetry matrix so that all eigenvalues is real. This matrix is a nonnegative matrix. The all diagonal entry from adjacency matrix is zero so that the trace is zero. Another representation matrix of the graph is the Laplacian matrix. Laplacian matrix is symmetry matrix and semidefinite positive so that all eigenvalues are real and non-negative. According to the spectral study in the graph, some that result is generalized to hypergraph. A hypergraph can be represented by a matrix such as adjacency, incidence, and Laplacian matrix. Throughout for this term, we use Laplacian matrix to represent a complete tripartite hypergraph. The aim from this research is to determine second smallest eigenvalues from this matrix and find a relation this eigenvalue with the connectivity of that hypergraph.

Keywords: Connectivity, graph, hypergraph, Laplacian matrix

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8 Normalized Laplacian Eigenvalues of Graphs

Authors: Shaowei Sun


Let G be a graph with vertex set V(G)={v_1,v_2,...,v_n} and edge set E(G). For any vertex v belong to V(G), let d_v denote the degree of v. The normalized Laplacian matrix of the graph G is the matrix where the non-diagonal (i,j)-th entry is -1/(d_id_j) when vertex i is adjacent to vertex j and 0 when they are not adjacent, and the diagonal (i,i)-th entry is the di. In this paper, we discuss some bounds on the largest and the second smallest normalized Laplacian eigenvalue of trees and graphs. As following, we found some new bounds on the second smallest normalized Laplacian eigenvalue of tree T in terms of graph parameters. Moreover, we use Sage to give some conjectures on the second largest and the third smallest normalized eigenvalues of graph.

Keywords: tree, graph, normalized Laplacian eigenvalues, normalized Laplacian matrix

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7 Complete Tripartite Graphs with Spanning Maximal Planar Subgraphs

Authors: Severino Gervacio, Velimor Almonte, Emmanuel Natalio


A simple graph is planar if it there is a way of drawing it in the plane without edge crossings. A planar graph which is not a proper spanning subgraph of another planar graph is a maximal planar graph. We prove that for complete tripartite graphs of order at most 9, the only ones that contain a spanning maximal planar subgraph are K1,1,1, K2,2,2, K2,3,3, and K3,3,3. The main result gives a necessary and sufficient condition for the complete tripartite graph Kx,y,z to contain a spanning maximal planar subgraph.

Keywords: graph, complete tripartite graph, maximal planar graph, planar graph, subgraph

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6 Travel Planning in Public Transport Networks Applying the Algorithm A* for Metropolitan District of Quito

Authors: M. Fernanda Salgado, Alfonso Tierra, Wilbert Aguilar


The present project consists in applying the informed search algorithm A star (A*) to solve traveler problems, applying it by urban public transportation routes. The digitization of the information allowed to identify 26% of the total of routes that are registered within the Metropolitan District of Quito. For the validation of this information, data were taken in field on the travel times and the difference with respect to the times estimated by the program, resulting in that the difference between them was not greater than 2:20 minutes. We validate A* algorithm with the Dijkstra algorithm, comparing nodes vectors based on the public transport stops, the validation was established through the student t-test hypothesis. Then we verified that the times estimated by the program using the A* algorithm are similar to those registered on field. Furthermore, we review the performance of the algorithm generating iterations in both algorithms. Finally, with these iterations, a hypothesis test was carried out again with student t-test where it was concluded that the iterations of the base algorithm Dijsktra are greater than those generated by the algorithm A*.

Keywords: Mobility, public transport, graph, routes, algorithm A*, travel planning

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5 Nonlinear Evolution on Graphs

Authors: Benniche Omar


We are concerned with abstract fully nonlinear differential equations having the form y’(t)=Ay(t)+f(t,y(t)) where A is an m—dissipative operator (possibly multi—valued) defined on a subset D(A) of a Banach space X with values in X and f is a given function defined on I×X with values in X. We consider a graph K in I×X. We recall that K is said to be viable with respect to the above abstract differential equation if for each initial data in K there exists at least one trajectory starting from that initial data and remaining in K at least for a short time. The viability problem has been studied by many authors by using various techniques and frames. If K is closed, it is shown that a tangency condition, which is mainly linked to the dynamic, is crucial for viability. In the case when X is infinite dimensional, compactness and convexity assumptions are needed. In this paper, we are concerned with the notion of near viability for a given graph K with respect to y’(t)=Ay(t)+f(t,y(t)). Roughly speaking, the graph K is said to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)), if for each initial data in K there exists at least one trajectory remaining arbitrary close to K at least for short time. It is interesting to note that the near viability is equivalent to an appropriate tangency condition under mild assumptions on the dynamic. Adding natural convexity and compactness assumptions on the dynamic, we may recover the (exact) viability. Here we investigate near viability for a graph K in I×X with respect to y’(t)=Ay(t)+f(t,y(t)) where A and f are as above. We emphasis that the t—dependence on the perturbation f leads us to introduce a new tangency concept. In the base of a tangency conditions expressed in terms of that tangency concept, we formulate criteria for K to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)). As application, an abstract null—controllability theorem is given.

Keywords: graph, viability, abstract differential equation, tangency condition

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4 An Owen Value for Cooperative Games with Pairwise a Priori Incompatibilities

Authors: Jose M. Gallardo, Nieves Jimenez, Andres Jimenez-Losada, Esperanza Lebron


A game with a priori incompatibilities is a triple (N,v,g) where (N,v) is a cooperative game, and (N,g) is a graph which establishes initial incompatibilities between some players. In these games, the negotiation has two stages. In the first stage, players can only negotiate with others with whom they are compatible. In the second stage, the grand coalition will be formed. We introduce a value for these games. Given a game with a priori incompatibility (N,v,g), we consider the family of coalitions without incompatibility relations among their players. This family is a normal set system or coalition configuration Ig. Therefore, we can assign to each game with a priori incompatibilities (N,v,g) a game with coalition configuration (N,v, Ig). Now, in order to obtain a payoff vector for (N,v,g), it suffices to calculate a payoff vector for (N,v, Ig). To this end, we apply a value for games with coalition configuration. In our case, we will use the dual configuration value, which has been studied in the literature. With this method, we obtain a value for games with a priori incompatibilities, which is called the Owen value for a priori incompatibilities. We provide a characterization of this value.

Keywords: graph, independent set, Cooperative game, Shapley value, game with coalition configuration, Owen value

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3 The Vertex Degree Distance of One Vertex Union of the Cycle and the Star

Authors: Ying Wang, Haiyan Xie, Aoming Zhang


The degree distance of a graph is a graph invariant that is more sensitive than the Wiener index. In this paper, we calculate the vertex degree distances of one vertex union of the cycle and the star, and the degree distance of one vertex union of the cycle and the star. These results lay a foundation for further study on the extreme value of the vertex degree distances, and the distribution of the vertices with the extreme value in one vertex union of the cycle and the star.

Keywords: graph, degree distance, vertex-degree-distance, one vertex union of a cycle and a star

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2 An Optimized Approach to Generate the Possible States of Football Tournaments Final Table

Authors: Mouslem Damkhi


This paper focuses on possible states of a football tournament final table according to the number of participating teams. Each team holds a position in the table with which it is possible to determine the highest and lowest points for that team. This paper proposes an optimized search space based on the minimum and maximum number of points which can be gained by each team to produce and enumerate the possible states for a football tournament final table. The proposed search space minimizes producing the invalid states which cannot occur during a football tournament. The generated states are filtered by a validity checking algorithm which seeks to reach a tournament graph based on a generated state. Thus, the algorithm provides a way to determine which team’s wins, draws and loses values guarantee a particular table position. The paper also presents and discusses the experimental results of the approach on the tournaments with up to eight teams. Comparing with a blind search algorithm, our proposed approach reduces generating the invalid states up to 99.99%, which results in a considerable optimization in term of the execution time.

Keywords: Combinatorics, Enumeration, graph, tournament

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1 Intrusion Detection Based on Graph Oriented Big Data Analytics

Authors: Ahlem Abid, Farah Jemili


Intrusion detection has been the subject of numerous studies in industry and academia, but cyber security analysts always want greater precision and global threat analysis to secure their systems in cyberspace. To improve intrusion detection system, the visualisation of the security events in form of graphs and diagrams is important to improve the accuracy of alerts. In this paper, we propose an approach of an IDS based on cloud computing, big data technique and using a machine learning graph algorithm which can detect in real time different attacks as early as possible. We use the MAWILab intrusion detection dataset . We choose Microsoft Azure as a unified cloud environment to load our dataset on. We implement the k2 algorithm which is a graphical machine learning algorithm to classify attacks. Our system showed a good performance due to the graphical machine learning algorithm and spark structured streaming engine.

Keywords: Machine Learning, Intrusion Detection, graph, Apache Spark Streaming, k2 algorithm, MAWILab, Microsoft Azure Cloud

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