Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3342

Search results for: graph algorithm

3342 A New Graph Theoretic Problem with Ample Practical Applications

Authors: Mehmet Hakan Karaata

Abstract:

In this paper, we first coin a new graph theocratic problem with numerous applications. Second, we provide two algorithms for the problem. The first solution is using a brute-force techniques, whereas the second solution is based on an initial identification of the cycles in the given graph. We then provide a correctness proof of the algorithm. The applications of the problem include graph analysis, graph drawing and network structuring.

Keywords: algorithm, cycle, graph algorithm, graph theory, network structuring

Procedia PDF Downloads 284
3341 Predictive Analysis of Personnel Relationship in Graph Database

Authors: Kay Thi Yar, Khin Mar Lar Tun

Abstract:

Nowadays, social networks are so popular and widely used in all over the world. In addition, searching personal information of each person and searching connection between them (peoples’ relation in real world) becomes interesting issue in our society. In this paper, we propose a framework with three portions for exploring peoples’ relations from their connected information. The first portion focuses on the Graph database structure to store the connected data of peoples’ information. The second one proposes the graph database searching algorithm, the Modified-SoS-ACO (Sense of Smell-Ant Colony Optimization). The last portion proposes the Deductive Reasoning Algorithm to define two persons’ relationship. This study reveals the proper storage structure for connected information, graph searching algorithm and deductive reasoning algorithm to predict and analyze the personnel relationship from peoples’ relation in their connected information.

Keywords: personnel information, graph storage structure, graph searching algorithm, deductive reasoning algorithm

Procedia PDF Downloads 371
3340 Speedup Breadth-First Search by Graph Ordering

Authors: Qiuyi Lyu, Bin Gong

Abstract:

Breadth-First Search(BFS) is a core graph algorithm that is widely used for graph analysis. As it is frequently used in many graph applications, improve the BFS performance is essential. In this paper, we present a graph ordering method that could reorder the graph nodes to achieve better data locality, thus, improving the BFS performance. Our method is based on an observation that the sibling relationships will dominate the cache access pattern during the BFS traversal. Therefore, we propose a frequency-based model to construct the graph order. First, we optimize the graph order according to the nodes’ visit frequency. Nodes with high visit frequency will be processed in priority. Second, we try to maximize the child nodes overlap layer by layer. As it is proved to be NP-hard, we propose a heuristic method that could greatly reduce the preprocessing overheads. We conduct extensive experiments on 16 real-world datasets. The result shows that our method could achieve comparable performance with the state-of-the-art methods while the graph ordering overheads are only about 1/15.

Keywords: breadth-first search, BFS, graph ordering, graph algorithm

Procedia PDF Downloads 57
3339 Graph Codes - 2D Projections of Multimedia Feature Graphs for Fast and Effective Retrieval

Authors: Stefan Wagenpfeil, Felix Engel, Paul McKevitt, Matthias Hemmje

Abstract:

Multimedia Indexing and Retrieval is generally designed and implemented by employing feature graphs. These graphs typically contain a significant number of nodes and edges to reflect the level of detail in feature detection. A higher level of detail increases the effectiveness of the results but also leads to more complex graph structures. However, graph-traversal-based algorithms for similarity are quite inefficient and computation intensive, especially for large data structures. To deliver fast and effective retrieval, an efficient similarity algorithm, particularly for large graphs, is mandatory. Hence, in this paper, we define a graph-projection into a 2D space (Graph Code) as well as the corresponding algorithms for indexing and retrieval. We show that calculations in this space can be performed more efficiently than graph-traversals due to a simpler processing model and a high level of parallelization. In consequence, we prove that the effectiveness of retrieval also increases substantially, as Graph Codes facilitate more levels of detail in feature fusion. Thus, Graph Codes provide a significant increase in efficiency and effectiveness (especially for Multimedia indexing and retrieval) and can be applied to images, videos, audio, and text information.

Keywords: indexing, retrieval, multimedia, graph algorithm, graph code

Procedia PDF Downloads 70
3338 Graph Cuts Segmentation Approach Using a Patch-Based Similarity Measure Applied for Interactive CT Lung Image Segmentation

Authors: Aicha Majda, Abdelhamid El Hassani

Abstract:

Lung CT image segmentation is a prerequisite in lung CT image analysis. Most of the conventional methods need a post-processing to deal with the abnormal lung CT scans such as lung nodules or other lesions. The simplest similarity measure in the standard Graph Cuts Algorithm consists of directly comparing the pixel values of the two neighboring regions, which is not accurate because this kind of metrics is extremely sensitive to minor transformations such as noise or other artifacts problems. In this work, we propose an improved version of the standard graph cuts algorithm based on the Patch-Based similarity metric. The boundary penalty term in the graph cut algorithm is defined Based on Patch-Based similarity measurement instead of the simple intensity measurement in the standard method. The weights between each pixel and its neighboring pixels are Based on the obtained new term. The graph is then created using theses weights between its nodes. Finally, the segmentation is completed with the minimum cut/Max-Flow algorithm. Experimental results show that the proposed method is very accurate and efficient, and can directly provide explicit lung regions without any post-processing operations compared to the standard method.

Keywords: graph cuts, lung CT scan, lung parenchyma segmentation, patch-based similarity metric

Procedia PDF Downloads 98
3337 Topological Indices of Some Graph Operations

Authors: U. Mary

Abstract:

Let be a graph with a finite, nonempty set of objects called vertices together with a set of unordered pairs of distinct vertices of called edges. The vertex set is denoted by and the edge set by. Given two graphs and the wiener index of, wiener index for the splitting graph of a graph, the first Zagreb index of and its splitting graph, the 3-steiner wiener index of, the 3-steiner wiener index of a special graph are explored in this paper.

Keywords: complementary prism graph, first Zagreb index, neighborhood corona graph, steiner distance, splitting graph, steiner wiener index, wiener index

Procedia PDF Downloads 433
3336 A Graph Theoretic Algorithm for Bandwidth Improvement in Computer Networks

Authors: Mehmet Karaata

Abstract:

Given two distinct vertices (nodes) source s and target t of a graph G = (V, E), the two node-disjoint paths problem is to identify two node-disjoint paths between s ∈ V and t ∈ V . Two paths are node-disjoint if they have no common intermediate vertices. In this paper, we present an algorithm with O(m)-time complexity for finding two node-disjoint paths between s and t in arbitrary graphs where m is the number of edges. The proposed algorithm has a wide range of applications in ensuring reliability and security of sensor, mobile and fixed communication networks.

Keywords: disjoint paths, distributed systems, fault-tolerance, network routing, security

Procedia PDF Downloads 273
3335 Efficient Heuristic Algorithm to Speed Up Graphcut in Gpu for Image Stitching

Authors: Tai Nguyen, Minh Bui, Huong Ninh, Tu Nguyen, Hai Tran

Abstract:

GraphCut algorithm has been widely utilized to solve various types of computer vision problems. Its expensive computational cost encouraged many researchers to improve the speed of the algorithm. Recent works proposed schemes that work on parallel computing platforms such as CUDA. However, the problem of low convergence speed prevents the usage of GraphCut for real time applications. In this paper, we propose global suppression heuristic to boost the conver-gence process of the algorithm. A parallel implementation of GraphCut algorithm on CUDA designed for the image stitching problem is introduced. Our method achieves up to 3× time boost on the graph of size 80 × 480 compared to the best sequential GraphCut algorithm while achieving satisfactory stitched images, suitable for panorama applications. Our source code will be soon available for further research.

Keywords: CUDA, graph cut, image stitching, texture synthesis, maxflow/mincut algorithm

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3334 Memetic Algorithm for Solving the One-To-One Shortest Path Problem

Authors: Omar Dib, Alexandre Caminada, Marie-Ange Manier

Abstract:

The purpose of this study is to introduce a novel approach to solve the one-to-one shortest path problem. A directed connected graph is assumed in which all edges’ weights are positive. Our method is based on a memetic algorithm in which we combine a genetic algorithm (GA) and a variable neighborhood search method (VNS). We compare our approximate method with two exact algorithms Dijkstra and Integer Programming (IP). We made experimentations using random generated, complete and real graph instances. In most case studies, numerical results show that our method outperforms exact methods with 5% average gap to the optimality. Our algorithm’s average speed is 20-times faster than Dijkstra and more than 1000-times compared to IP. The details of the experimental results are also discussed and presented in the paper.

Keywords: shortest path problem, Dijkstra’s algorithm, integer programming, memetic algorithm

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3333 Survey Paper on Graph Coloring Problem and Its Application

Authors: Prateek Chharia, Biswa Bhusan Ghosh

Abstract:

Graph coloring is one of the prominent concepts in graph coloring. It can be defined as a coloring of the various regions of the graph such that all the constraints are fulfilled. In this paper various graphs coloring approaches like greedy coloring, Heuristic search for maximum independent set and graph coloring using edge table is described. Graph coloring can be used in various real time applications like student time tabling generation, Sudoku as a graph coloring problem, GSM phone network.

Keywords: graph coloring, greedy coloring, heuristic search, edge table, sudoku as a graph coloring problem

Procedia PDF Downloads 445
3332 Intrusion Detection Based on Graph Oriented Big Data Analytics

Authors: Ahlem Abid, Farah Jemili

Abstract:

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: Apache Spark Streaming, Graph, Intrusion detection, k2 algorithm, Machine Learning, MAWILab, Microsoft Azure Cloud

Procedia PDF Downloads 61
3331 Matching on Bipartite Graphs with Applications to School Course Registration Systems

Authors: Zhihan Li

Abstract:

Nowadays, most universities use the course enrollment system considering students’ registration orders. However, the students’ preference level to certain courses is also one important factor to consider. In this research, the possibility of applying a preference-first system has been discussed and analyzed compared to the order-first system. A bipartite graph is applied to resemble the relationship between students and courses they tend to register. With the graph set up, we apply Ford-Fulkerson (F.F.) Algorithm to maximize parings between two sets of nodes, in our case, students and courses. Two models are proposed in this paper: the one considered students’ order first, and the one considered students’ preference first. By comparing and contrasting the two models, we highlight the usability of models which potentially leads to better designs for school course registration systems.

Keywords: bipartite graph, Ford-Fulkerson (F.F.) algorithm, graph theory, maximum matching

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3330 Complete Tripartite Graphs with Spanning Maximal Planar Subgraphs

Authors: Severino Gervacio, Velimor Almonte, Emmanuel Natalio

Abstract:

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

Procedia PDF Downloads 241
3329 Efficient Filtering of Graph Based Data Using Graph Partitioning

Authors: Nileshkumar Vaishnav, Aditya Tatu

Abstract:

An algebraic framework for processing graph signals axiomatically designates the graph adjacency matrix as the shift operator. In this setup, we often encounter a problem wherein we know the filtered output and the filter coefficients, and need to find out the input graph signal. Solution to this problem using direct approach requires O(N3) operations, where N is the number of vertices in graph. In this paper, we adapt the spectral graph partitioning method for partitioning of graphs and use it to reduce the computational cost of the filtering problem. We use the example of denoising of the temperature data to illustrate the efficacy of the approach.

Keywords: graph signal processing, graph partitioning, inverse filtering on graphs, algebraic signal processing

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3328 Research on Dynamic Practical Byzantine Fault Tolerance Consensus Algorithm

Authors: Cao Xiaopeng, Shi Linkai

Abstract:

The practical Byzantine fault-tolerant algorithm does not add nodes dynamically. It is limited in practical application. In order to add nodes dynamically, Dynamic Practical Byzantine Fault Tolerance Algorithm (DPBFT) was proposed. Firstly, a new node sends request information to other nodes in the network. The nodes in the network decide their identities and requests. Then the nodes in the network reverse connect to the new node and send block information of the current network. The new node updates information. Finally, the new node participates in the next round of consensus, changes the view and selects the master node. This paper abstracts the decision of nodes into the undirected connected graph. The final consistency of the graph is used to prove that the proposed algorithm can adapt to the network dynamically. Compared with the PBFT algorithm, DPBFT has better fault tolerance and lower network bandwidth.

Keywords: practical byzantine, fault tolerance, blockchain, consensus algorithm, consistency analysis

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3327 An Optimized Association Rule Mining Algorithm

Authors: Archana Singh, Jyoti Agarwal, Ajay Rana

Abstract:

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: association rules, data mining, dynamic item set counting, FP-growth, friendly algorithm, graph

Procedia PDF Downloads 347
3326 Improvement a Lower Bound of Energy for Some Family of Graphs, Related to Determinant of Adjacency Matrix

Authors: Saieed Akbari, Yousef Bagheri, Amir Hossein Ghodrati, Sima Saadat Akhtar

Abstract:

Let G be a simple graph with the vertex set V (G) and with the adjacency matrix A (G). The energy E (G) of G is defined to be the sum of the absolute values of all eigenvalues of A (G). Also let n and m be number of edges and vertices of the graph respectively. A regular graph is a graph where each vertex has the same number of neighbours. Given a graph G, its line graph L(G) is a graph such that each vertex of L(G) represents an edge of G; and two vertices of L(G) are adjacent if and only if their corresponding edges share a common endpoint in G. In this paper we show that for every regular graphs and also for every line graphs such that (G) 3 we have, E(G) 2nm + n 1. Also at the other part of the paper we prove that 2 (G) E(G) for an arbitrary graph G.

Keywords: eigenvalues, energy, line graphs, matching number

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3325 Optimal Management of Internal Capital of Company

Authors: S. Sadallah

Abstract:

In this paper, dynamic programming is used to determine the optimal management of financial resources in company. Solution of the problem by consider into simpler substructures is constructed. The optimal management of internal capital of company are simulated. The tools applied in this development are based on graph theory. The software of given problems is built by using greedy algorithm. The obtained model and program maintenance enable us to define the optimal version of management of proper financial flows by using visual diagram on each level of investment.

Keywords: management, software, optimal, greedy algorithm, graph-diagram

Procedia PDF Downloads 218
3324 An Algorithm to Find Fractional Edge Domination Number and Upper Fractional Edge Domination Number of an Intuitionistic Fuzzy Graph

Authors: Karunambigai Mevani Govindasamy, Sathishkumar Ayyappan

Abstract:

In this paper, we formulate the algorithm to find out the dominating function parameters of Intuitionistic Fuzzy Graphs(IFG). The methodology we adopted here is converting any physical problem into an IFG, and that has been transformed into Intuitionistic Fuzzy Matrix. Using Linear Program Solver software (LiPS), we found the defined parameters for the given IFG. We obtained these parameters for a path and cycle IFG. This study can be extended to other varieties of IFG. In particular, we obtain the definition of edge dominating function, minimal edge dominating function, fractional edge domination number (γ_if^') and upper fractional edge domination number (Γ_if^') of an intuitionistic fuzzy graph. Also, we formulated an algorithm which is appropriate to work on LiPS to find fractional edge domination number and upper fractional edge domination number of an IFG.

Keywords: fractional edge domination number, intuitionistic fuzzy cycle, intuitionistic fuzzy graph, intuitionistic fuzzy path

Procedia PDF Downloads 75
3323 Deciding Graph Non-Hamiltonicity via a Closure Algorithm

Authors: E. R. Swart, S. J. Gismondi, N. R. Swart, C. E. Bell

Abstract:

We present an heuristic algorithm that decides graph non-Hamiltonicity. All graphs are directed, each undirected edge regarded as a pair of counter directed arcs. Each of the n! Hamilton cycles in a complete graph on n+1 vertices is mapped to an n-permutation matrix P where p(u,i)=1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n+1. We first create exclusion set E by noting all arcs (u, v) not in G, sufficient to code precisely all cycles excluded from G i.e. cycles not in G use at least one arc not in G. Members are pairs of components of P, {p(u,i),p(v,i+1)}, i=1, n-1. A doubly stochastic-like relaxed LP formulation of the Hamilton cycle decision problem is constructed. Each {p(u,i),p(v,i+1)} in E is coded as variable q(u,i,v,i+1)=0 i.e. shrinks the feasible region. We then implement the Weak Closure Algorithm (WCA) that tests necessary conditions of a matching, together with Boolean closure to decide 0/1 variable assignments. Each {p(u,i),p(v,j)} not in E is tested for membership in E, and if possible, added to E (q(u,i,v,j)=0) to iteratively maximize |E|. If the WCA constructs E to be maximal, the set of all {p(u,i),p(v,j)}, then G is decided non-Hamiltonian. Only non-Hamiltonian G share this maximal property. Ten non-Hamiltonian graphs (10 through 104 vertices) and 2000 randomized 31 vertex non-Hamiltonian graphs are tested and correctly decided non-Hamiltonian. For Hamiltonian G, the complement of E covers a matching, perhaps useful in searching for cycles. We also present an example where the WCA fails.

Keywords: Hamilton cycle decision problem, computational complexity theory, graph theory, theoretical computer science

Procedia PDF Downloads 295
3322 Graph Similarity: Algebraic Model and Its Application to Nonuniform Signal Processing

Authors: Nileshkumar Vishnav, Aditya Tatu

Abstract:

A recent approach of representing graph signals and graph filters as polynomials is useful for graph signal processing. In this approach, the adjacency matrix plays pivotal role; instead of the more common approach involving graph-Laplacian. In this work, we follow the adjacency matrix based approach and corresponding algebraic signal model. We further expand the theory and introduce the concept of similarity of two graphs. The similarity of graphs is useful in that key properties (such as filter-response, algebra related to graph) get transferred from one graph to another. We demonstrate potential applications of the relation between two similar graphs, such as nonuniform filter design, DTMF detection and signal reconstruction.

Keywords: graph signal processing, algebraic signal processing, graph similarity, isospectral graphs, nonuniform signal processing

Procedia PDF Downloads 264
3321 Metric Dimension on Line Graph of Honeycomb Networks

Authors: M. Hussain, Aqsa Farooq

Abstract:

Let G = (V,E) be a connected graph and distance between any two vertices a and b in G is a−b geodesic and is denoted by d(a, b). A set of vertices W resolves a graph G if each vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G. In this paper line graph of honeycomb network has been derived and then we calculated the metric dimension on line graph of honeycomb network.

Keywords: Resolving set, Metric dimension, Honeycomb network, Line graph

Procedia PDF Downloads 92
3320 Automatic LV Segmentation with K-means Clustering and Graph Searching on Cardiac MRI

Authors: Hae-Yeoun Lee

Abstract:

Quantification of cardiac function is performed by calculating blood volume and ejection fraction in routine clinical practice. However, these works have been performed by manual contouring,which requires computational costs and varies on the observer. In this paper, an automatic left ventricle segmentation algorithm on cardiac magnetic resonance images (MRI) is presented. Using knowledge on cardiac MRI, a K-mean clustering technique is applied to segment blood region on a coil-sensitivity corrected image. Then, a graph searching technique is used to correct segmentation errors from coil distortion and noises. Finally, blood volume and ejection fraction are calculated. Using cardiac MRI from 15 subjects, the presented algorithm is tested and compared with manual contouring by experts to show outstanding performance.

Keywords: cardiac MRI, graph searching, left ventricle segmentation, K-means clustering

Procedia PDF Downloads 336
3319 On the Zeros of the Degree Polynomial of a Graph

Authors: S. R. Nayaka, Putta Swamy

Abstract:

Graph polynomial is one of the algebraic representations of the Graph. The degree polynomial is one of the simple algebraic representations of graphs. The degree polynomial of a graph G of order n is the polynomial Deg(G, x) with the coefficients deg(G,i) where deg(G,i) denotes the number of vertices of degree i in G. In this article, we investigate the behavior of the roots of some families of Graphs in the complex field. We investigate for the graphs having only integral roots. Further, we characterize the graphs having single roots or having real roots and behavior of the polynomial at the particular value is also obtained.

Keywords: degree polynomial, regular graph, minimum and maximum degree, graph operations

Procedia PDF Downloads 157
3318 From Convexity in Graphs to Polynomial Rings

Authors: Ladznar S. Laja, Rosalio G. Artes, Jr.

Abstract:

This paper introduced a graph polynomial relating convexity concepts. A graph polynomial is a polynomial representing a graph given some parameters. On the other hand, a subgraph H of a graph G is said to be convex in G if for every pair of vertices in H, every shortest path with these end-vertices lies entirely in H. We define the convex subgraph polynomial of a graph G to be the generating function of the sequence of the numbers of convex subgraphs of G of cardinalities ranging from zero to the order of G. This graph polynomial is monic since G itself is convex. The convex index which counts the number of convex subgraphs of G of all orders is just the evaluation of this polynomial at 1. Relationships relating algebraic properties of convex subgraphs polynomial with graph theoretic concepts are established.

Keywords: convex subgraph, convex index, generating function, polynomial ring

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3317 An Approach to Maximize the Influence Spread in the Social Networks

Authors: Gaye Ibrahima, Mendy Gervais, Seck Diaraf, Ouya Samuel

Abstract:

In this paper, we consider the influence maximization in social networks. Here we give importance to initial diffuser called the seeds. The goal is to find efficiently a subset of k elements in the social network that will begin and maximize the information diffusion process. A new approach which treats the social network before to determine the seeds, is proposed. This treatment eliminates the information feedback toward a considered element as seed by extracting an acyclic spanning social network. At first, we propose two algorithm versions called SCG − algoritm (v1 and v2) (Spanning Connected Graphalgorithm). This algorithm takes as input data a connected social network directed or no. And finally, a generalization of the SCG − algoritm is proposed. It is called SG − algoritm (Spanning Graph-algorithm) and takes as input data any graph. These two algorithms are effective and have each one a polynomial complexity. To show the pertinence of our approach, two seeds set are determined and those given by our approach give a better results. The performances of this approach are very perceptible through the simulation carried out by the R software and the igraph package.

Keywords: acyclic spanning graph, centrality measures, information feedback, influence maximization, social network

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3316 An Application of Graph Theory to The Electrical Circuit Using Matrix Method

Authors: Samai'la Abdullahi

Abstract:

A graph is a pair of two set and so that a graph is a pictorial representation of a system using two basic element nodes and edges. A node is represented by a circle (either hallo shade) and edge is represented by a line segment connecting two nodes together. In this paper, we present a circuit network in the concept of graph theory application and also circuit models of graph are represented in logical connection method were we formulate matrix method of adjacency and incidence of matrix and application of truth table.

Keywords: euler circuit and path, graph representation of circuit networks, representation of graph models, representation of circuit network using logical truth table

Procedia PDF Downloads 476
3315 Building 1-Well-Covered Graphs by Corona, Join, and Rooted Product of Graphs

Authors: Vadim E. Levit, Eugen Mandrescu

Abstract:

A graph is well-covered if all its maximal independent sets are of the same size. A well-covered graph is 1-well-covered if deletion of every vertex of the graph leaves it well-covered. It is known that a graph without isolated vertices is 1-well-covered if and only if every two disjoint independent sets are included in two disjoint maximum independent sets. Well-covered graphs are related to combinatorial commutative algebra (e.g., every Cohen-Macaulay graph is well-covered, while each Gorenstein graph without isolated vertices is 1-well-covered). Our intent is to construct several infinite families of 1-well-covered graphs using the following known graph operations: corona, join, and rooted product of graphs. Adopting some known techniques used to advantage for well-covered graphs, one can prove that: if the graph G has no isolated vertices, then the corona of G and H is 1-well-covered if and only if H is a complete graph of order two at least; the join of the graphs G and H is 1-well-covered if and only if G and H have the same independence number and both are 1-well-covered; if H satisfies the property that every three pairwise disjoint independent sets are included in three pairwise disjoint maximum independent sets, then the rooted product of G and H is 1-well-covered, for every graph G. These findings show not only how to generate some more families of 1-well-covered graphs, but also that, to this aim, sometimes, one may use graphs that are not necessarily 1-well-covered.

Keywords: maximum independent set, corona, concatenation, join, well-covered graph

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3314 Computing Maximum Uniquely Restricted Matchings in Restricted Interval Graphs

Authors: Swapnil Gupta, C. Pandu Rangan

Abstract:

A uniquely restricted matching is defined to be a matching M whose matched vertices induces a sub-graph which has only one perfect matching. In this paper, we make progress on the open question of the status of this problem on interval graphs (graphs obtained as the intersection graph of intervals on a line). We give an algorithm to compute maximum cardinality uniquely restricted matchings on certain sub-classes of interval graphs. We consider two sub-classes of interval graphs, the former contained in the latter, and give O(|E|^2) time algorithms for both of them. It is to be noted that both sub-classes are incomparable to proper interval graphs (graphs obtained as the intersection graph of intervals in which no interval completely contains another interval), on which the problem can be solved in polynomial time.

Keywords: uniquely restricted matching, interval graph, matching, induced matching, witness counting

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3313 Top-K Shortest Distance as a Similarity Measure

Authors: Andrey Lebedev, Ilya Dmitrenok, JooYoung Lee, Leonard Johard

Abstract:

Top-k shortest path routing problem is an extension of finding the shortest path in a given network. Shortest path is one of the most essential measures as it reveals the relations between two nodes in a network. However, in many real world networks, whose diameters are small, top-k shortest path is more interesting as it contains more information about the network topology. Many variations to compute top-k shortest paths have been studied. In this paper, we apply an efficient top-k shortest distance routing algorithm to the link prediction problem and test its efficacy. We compare the results with other base line and state-of-the-art methods as well as with the shortest path. Then, we also propose a top-k distance based graph matching algorithm.

Keywords: graph matching, link prediction, shortest path, similarity

Procedia PDF Downloads 283