Search results for: Vertex covering Problem

Authors: Fatma A. Karkory, Ali A. Abudalmola

Abstract:

The travelling salesman problem (TSP) is a combinatorial optimization problem in which the goal is to find the shortest path between different cities that the salesman takes. In other words, the problem deals with finding a route covering all cities so that total distance and execution time is minimized. This paper adopts the nearest neighbor and minimum spanning tree algorithm to solve the well-known travelling salesman problem. The algorithms were implemented using java programming language. The approach is tested on three graphs that making a TSP tour instance of 5-city, 10 –city, and 229–city. The computation results validate the performance of the proposed algorithm.

Keywords: Heuristics, minimum spanning tree algorithm, Nearest Neighbor, Travelling Salesman Problem (TSP).

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Authors: Wongsakorn Charoenpanitseri

Abstract:

The total chromatic number χ"(G) of a graph G is the minimum number of colors needed to color the elements (vertices and edges) of G such that no incident or adjacent pair of elements receive the same color Let G be a graph with maximum degree Δ(G). Considering a total coloring of G and focusing on a vertex with maximum degree. A vertex with maximum degree needs a color and all Δ(G) edges incident to this vertex need more Δ(G) + 1 distinct colors. To color all vertices and all edges of G, it requires at least Δ(G) + 1 colors. That is, χ"(G) is at least Δ(G) + 1. However, no one can find a graph G with the total chromatic number which is greater than Δ(G) + 2. The Total Coloring Conjecture states that for every graph G, χ"(G) is at most Δ(G) + 2. In this paper, we prove that the Total Coloring Conjectur for a Δ-claw-free 3-degenerated graph. That is, we prove that the total chromatic number of every Δ-claw-free 3-degenerated graph is at most Δ(G) + 2.

Keywords: Total colorings, the total chromatic number, 3-degenerated.

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Authors: Sammani Danwawu Abdullahi

Abstract:

Vertex Enumeration Algorithms explore the methods and procedures of generating the vertices of general polyhedra formed by system of equations or inequalities. These problems of enumerating the extreme points (vertices) of general polyhedra are shown to be NP-Hard. This lead to exploring how to count the vertices of general polyhedra without listing them. This is also shown to be #P-Complete. Some fully polynomial randomized approximation schemes (fpras) of counting the vertices of some special classes of polyhedra associated with Down-Sets, Independent Sets, 2-Knapsack problems and 2 x n transportation problems are presented together with some discovered open problems.

Keywords: Approximation, counting with uncertainties, mathematical programming, optimization, vertex enumeration.

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Authors: H. V. Chen

Abstract:

Assume that we have m identical graphs where the graphs consists of paths with k vertices where k is a positive integer. In this paper, we discuss certain labelling of the m graphs called c-Erdösian for some positive integers c. We regard labellings of the vertices of the graphs by positive integers, which induce the edge labels for the paths as the sum of the two incident vertex labels. They have the property that each vertex label and edge label appears only once in the set of positive integers {c, . . . , c+6m- 1}. Here, we show how to construct certain c-Erdösian of m paths with 2 and 3 vertices by using Skolem sequences.

Keywords: c-Erdösian, Skolem sequences, magic labelling

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Authors: M. Amiri

Abstract:

In this work, functionally graded materials (FGMs), subjected to loading, which varies with time has been studied. The material properties of FGM are changing through the thickness of material as power law distribution. The conical shells have been chosen for this study so in the first step capability equations for FGM have been obtained. With Galerkin method, these equations have been replaced with time dependant differential equations with variable coefficient. These equations have solved for different initial conditions with variation methods. Important parameters in loading conditions are semi-vertex angle, external pressure and material properties. Results validation has been done by comparison between with those in previous studies of other researchers.

Keywords: Impulsive semi-vertex angle, loading, functionally graded materials, composite material.

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Authors: Wen-Yin Huang, Jia-Jie Liu, Jou-Ming Chang

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Faults in a network may take various forms such as hardware/software errors, vertex/edge faults, etc. Folded hypercube is a well-known variation of the hypercube structure and can be constructed from a hypercube by adding a link to every pair of nodes with complementary addresses. Let FFv (respectively, FFe) be the set of faulty nodes (respectively, faulty links) in an n-dimensional folded hypercube FQn. Hsieh et al. have shown that FQn - FFv - FFe for n ≥ 3 contains a fault-free cycle of length at least 2n -2|FFv|, under the constraints that (1) |FFv| + |FFe| ≤ 2n - 4 and (2) every node in FQn is incident to at least two fault-free links. In this paper, we further consider the constraints |FFv| + |FFe| ≤ 2n - 3. We prove that FQn - FFv - FFe for n ≥ 5 still has a fault-free cycle of length at least 2n - 2|FFv|, under the constraints : (1) |FFv| + |FFe| ≤ 2n - 3, (2) |FFe| ≥ n + 2, and (3) every vertex is still incident with at least two links.

Keywords: Folded hypercubes, interconnection networks, cycle embedding, faulty elements.

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Authors: Clara Shenderey, Helena Vitoshkin, Mordechai Barak, Avraham Arbel

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Greenhouse cultivation is an energy-intensive process due to the high demands on cooling or heating according to external climatic conditions, which could be extreme in the summer or winter seasons. The thermal radiation rate inside a greenhouse depends mainly on the type of covering material and greenhouse construction. Using additional thermal screens under a greenhouse covering combined with a dehumidification system improves the insulation and could be cost-effective. Greenhouse covering material usually contains protective ultraviolet (UV) radiation additives to prevent the film wear, insect harm, and crop diseases. This paper investigates the overall heat transfer coefficient, or U-value, for greenhouse polyethylene covering contains UV-additives and glass covering with or without a thermal screen supplement. The hot-box method was employed to evaluate overall heat transfer coefficients experimentally as a function of the type and number of the thermal screens. The results show that the overall heat transfer coefficient decreases with increasing the number of thermal screens as a hyperbolic function. The overall heat transfer coefficient highly depends on the ability of the material to reflect thermal radiation. Using a greenhouse covering, i.e., polyethylene films or glass, in combination with high reflective thermal screens, i.e., containing about 98% of aluminum stripes or aluminum foil, the U-value reduces by 61%-89% in the first case, whereas by 70%-92% in the second case, depending on the number of the thermal screen. Using thermal screens made from low reflective materials may reduce the U-value by 30%-57%. The heat transfer coefficient is an indicator of the thermal insulation properties of the materials, which allows farmers to make decisions on the use of appropriate thermal screens depending on the external and internal climate conditions in a greenhouse.

Keywords: Energy-saving thermal screen, greenhouse covering material, heat transfer coefficient, hot box.

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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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Authors: Ahmad M. Awwad, Jehad Al-Sadi

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The star network is one of the promising interconnection networks for future high speed parallel computers, it is expected to be one of the future-generation networks. The star network is both edge and vertex symmetry, it was shown to have many gorgeous topological proprieties also it is owns hierarchical structure framework. Although much of the research work has been done on this promising network in literature, it still suffers from having enough algorithms for load balancing problem. In this paper we try to work on this issue by investigating and proposing an efficient algorithm for load balancing problem for the star network. The proposed algorithm is called Star Clustered Dimension Exchange Method SCDEM to be implemented on the star network. The proposed algorithm is based on the Clustered Dimension Exchange Method (CDEM). The SCDEM algorithm is shown to be efficient in redistributing the load balancing as evenly as possible among all nodes of different factor networks.

Keywords: Interconnection networks, Load balancing, Star network.

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Authors: S. Mulholland

Abstract:

Octree compression techniques have been used for several years for compressing large three dimensional data sets into homogeneous regions. This compression technique is ideally suited to datasets which have similar values in clusters. Oil engineers represent reservoirs as a three dimensional grid where hydrocarbons occur naturally in clusters. This research looks at the efficiency of storing these grids using octree compression techniques where grid cells are broken into active and inactive regions. Initial experiments yielded high compression ratios as only active leaf nodes and their ancestor, header nodes are stored as a bitstream to file on disk. Savings in computational time and memory were possible at decompression, as only active leaf nodes are sent to the graphics card eliminating the need of reconstructing the original matrix. This results in a more compact vertex table, which can be loaded into the graphics card quicker and generating shorter refresh delay times.

Keywords: 3D visualisation, compressed vertex tables, octree compression techniques, oil reservoir grids.

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Authors: Hui-Chuan Lu

Abstract:

A perfect secret-sharing scheme is a method to distribute a secret among a set of participants in such a way that only qualified subsets of participants can recover the secret and the joint share of participants in any unqualified subset is statistically independent of the secret. The collection of all qualified subsets is called the access structure of the perfect secret-sharing scheme. In a graph-based access structure, each vertex of a graph G represents a participant and each edge of G represents a minimal qualified subset. The average information ratio of a perfect secret-sharing scheme  realizing the access structure based on G is defined as AR = (Pv2V (G) H(v))/(|V (G)|H(s)), where s is the secret and v is the share of v, both are random variables from  and H is the Shannon entropy. The infimum of the average information ratio of all possible perfect secret-sharing schemes realizing a given access structure is called the optimal average information ratio of that access structure. Most known results about the optimal average information ratio give upper bounds or lower bounds on it. In this present structures based on bipartite graphs and determine the exact values of the optimal average information ratio of some infinite classes of them.

Keywords: secret-sharing scheme, average information ratio, star covering, core sequence.

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Authors: Hui-Chuan Lu

Abstract:

In a perfect secret-sharing scheme, a dealer distributes a secret among a set of participants in such a way that only qualified subsets of participants can recover the secret and the joint share of the participants in any unqualified subset is statistically independent of the secret. The access structure of the scheme refers to the collection of all qualified subsets. In a graph-based access structures, each vertex of a graph G represents a participant and each edge of G represents a minimal qualified subset. The average information ratio of a perfect secret-sharing scheme realizing a given access structure is the ratio of the average length of the shares given to the participants to the length of the secret. The infimum of the average information ratio of all possible perfect secret-sharing schemes realizing an access structure is called the optimal average information ratio of that access structure. We study the optimal average information ratio of the access structures based on bipartite graphs. Based on some previous results, we give a bound on the optimal average information ratio for all bipartite graphs of girth at least six. This bound is the best possible for some classes of bipartite graphs using our approach.

Keywords: Secret-sharing scheme, average information ratio, star covering, deduction, core cluster.

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Authors: M. Heck, H. Vettiger

Abstract:

Small and medium-sized enterprises (SME) are the backbone of central Europe’s economies and have a significant contribution to the gross domestic product. Production planning and scheduling (PPS) is still a crucial element in manufacturing industries of the 21^st century even though this area of research is more than a century old. The topic of PPS is well researched especially in the context of large enterprises in the manufacturing industry. However the implementation of PPS methodologies within SME is mostly unobserved. This work analyzes how PPS is implemented in SME with the geographical focus on Switzerland and its vicinity. Based on restricted resources compared to large enterprises, SME have to face different challenges. The real problem areas of selected enterprises in regards of PPS are identified and evaluated. For the identified real-life problem areas of SME clear and detailed recommendations are created, covering concepts and best practices and the efficient usage of PPS. Furthermore the economic and entrepreneurial value for companies is lined out and why the implementation of the introduced recommendations is advised.

Keywords: Central Europe, PPS, Production Planning, SME.

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Authors: Yuan-Kang Shih, Shu-Li Chang, Shin-Shin Kao

Abstract:

Qk n has been shown as an alternative to the hypercube family. For any even integer k ≥ 4 and any integer n ≥ 2, Qk n is a bipartite graph. In this paper, we will prove that given any pair of vertices, w and b, from different partite sets of Qk n, there exist 2n internally disjoint paths between w and b, denoted by {Pi | 0 ≤ i ≤ 2n-1}, such that 2n-1 i=0 Pi covers all vertices of Qk n. The result is optimal since each vertex of Qk n has exactly 2n neighbors.

Keywords: container, Hamiltonian, k-ary n-cube, m*-connected.

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Authors: V. Goremikins, K. Rocens, D. Serdjuks

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Suspended cable structures are most preferable for large spans covering due to rational use of structural materials, but the problem of suspended cable structures is initial shape change under the action of non-symmetrical load. The problem can be solved by increasing of relation of dead weight and imposed load, but this methods cause increasing of materials consumption.Prestressed cable truss usage is another way how the problem of shape change under the action of non-symmetrical load can be fixed. The better results can be achieved if we replace top chord with cable truss with cross web. Rational structure of the cable truss for prestressed cable truss top chord was developed using optimization realized in FEM program ANSYS 12 environment. Single cable and cable truss model work was discovered.Analytical and model testing results indicate, that usage of cable truss with the cross web as a top chord of prestressed cable truss instead of single cable allows to reduce total displacements by 13-16% in the case of non-symmetrical load. In case of uniformly distributed load single cable is preferable.

Keywords: Cable trusses, Non-symmetrical load, Cable truss models, Vertical displacements

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Authors: Minghui Wang, Shanrui Hu

Abstract:

An inverse problem of doubly center matrices is discussed. By translating the constrained problem into unconstrained problem, two iterative methods are proposed. A numerical example illustrate our algorithms.

Keywords: doubly center matrix, electric network theory, iterative methods, least-square problem.

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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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Authors: Nitima Aschariyaphotha, Pratan Sakkaplangkul, Anirut Luadsong

Abstract:

The study of the Andaman Sea can be studied by using the oceanic model; therefore the grid covering the study area should be generated. This research aims to generate grid covering the Andaman Sea, situated between longitudes 90◦E to 101◦E and latitudes 1◦N to 18◦N. A horizontal grid is an orthogonal curvilinear with 87 × 217 grid points. The methods used in this study are cubic spline and bilinear interpolations. The boundary grid points are generated by spline interpolation while the interior grid points have to be specified by bilinear interpolation method. A vertical grid is sigma coordinate with 15 layers of water column.

Keywords: Sigma Coordinate, Curvilinear Coordinate, AndamanSea.

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Authors: Xiantong Li, Jianzhong Li

Abstract:

Graph has become increasingly important in modeling complicated structures and schemaless data such as proteins, chemical compounds, and XML documents. Given a graph query, it is desirable to retrieve graphs quickly from a large database via graph-based indices. Different from the existing methods, our approach, called VFM (Vertex to Frequent Feature Mapping), makes use of vertices and decision features as the basic indexing feature. VFM constructs two mappings between vertices and frequent features to answer graph queries. The VFM approach not only provides an elegant solution to the graph indexing problem, but also demonstrates how database indexing and query processing can benefit from data mining, especially frequent pattern mining. The results show that the proposed method not only avoids the enumeration method of getting subgraphs of query graph, but also effectively reduces the subgraph isomorphism tests between the query graph and graphs in candidate answer set in verification stage.

Keywords: Decision Feature, Frequent Feature, Graph Dataset, Graph Query

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Authors: Chao Wang, Ting-Zhu Huang Chen Jia

Abstract:

In this paper, we propose a new linear complementarity problem named as bi-linear complementarity problem (BLCP) and the method for solving BLCP. In addition, the algorithm for error estimation of BLCP is also given. Numerical experiments show that the algorithm is efficient.

Keywords: Bi-linear complementarity problem, Linear complementarity problem, Extended linear complementarity problem, Error estimation, P-matrix, M-matrix.

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Authors: Sukhveer Singh, Sandeep Singh

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A bi-objective fuzzy transportation problem with the objectives to minimize the total fuzzy cost and fuzzy time of transportation without according priorities to them is considered. To the best of our knowledge, there is no method in the literature to find efficient solutions of the bi-objective transportation problem under uncertainty. In this paper, a bi-objective transportation problem in an uncertain environment has been formulated. An algorithm has been proposed to find efficient solutions of the bi-objective transportation problem under uncertainty. The proposed algorithm avoids the degeneracy and gives the optimal solution faster than other existing algorithms for the given uncertain transportation problem.

Keywords: Transportation problem, efficient solution, ranking function, fuzzy transportation problem.

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Authors: Kenza Aida Amara, Bachir Djebbar

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We treat the two-dimensional bin packing problem which involves packing a given set of rectangles into a minimum number of larger identical rectangles called bins. This combinatorial problem is NP-hard. We propose a pretreatment for the oriented version of the problem that allows the valorization of the lost areas in the bins and the reduction of the size problem. A heuristic method based on the strategy first-fit adapted to this problem is presented. We present an approach of resolution by bee colony optimization. Computational results express a comparison of the number of bins used with and without pretreatment.

Keywords: Bee colony optimization, bin packing, heuristic algorithm, pretreatment.

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Authors: Ahmad Salehi

Abstract:

An acyclic coloring of a graph G is a coloring of its vertices such that:(i) no two neighbors in G are assigned the same color and (ii) no bicolored cycle can exist in G. The acyclic chromatic number of G is the least number of colors necessary to acyclically color G. Recently it has been proved that any graph of maximum degree 5 has an acyclic chromatic number at most 8. In this paper we present another proof for this result.

Keywords: Acyclic Coloring, Vertex coloring.

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Authors: Tsuyoshi Okita, Tatsuya Niwa

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For a given specific problem an efficient algorithm has been the matter of study. However, an alternative approach orthogonal to this approach comes out, which is called a reduction. In general for a given specific problem this reduction approach studies how to convert an original problem into subproblems. This paper proposes a formal modeling language to support this reduction approach. We show three examples from the wide area of learning problems. The benefit is a fast prototyping of algorithms for a given new problem.

Keywords: Formal language, statistical inference problem, reduction.

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Authors: S. Babitha, J. Baskar Babujee

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A prime cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2, ..., |V |} such that each edge uv is assigned the label 1 if gcd(f(u), f(v)) = 1 and 0 if gcd(f(u), f(v)) > 1, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. In this paper we exhibit some characterization results and new constructions on prime cordial graphs.

Keywords: Prime cordial, tree, Euler, bijective, function.

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Authors: M. Ahmad, M. Gourgand, C. Caux

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The Resource-Constrained Project Scheduling Problem (RCPSP) is concerned with single-item or small batch production where limited resources have to be allocated to dependent activities over time. Over the past few decades, a lot of work has been made with the use of optimal solution procedures for this basic problem type and its extensions. Brucker and Knust[1] discuss, how timetabling problems can be modeled as a RCPSP. Authors discuss high school timetabling and university course timetabling problem as an example. We have formulated two mathematical formulations of course timetabling problem in a new way which are the prototype of single-mode RCPSP. Our focus is to show, how course timetabling problem can be transformed into RCPSP. We solve this transformation model with genetic algorithm.

Keywords: Course Timetabling, Integer programming, Combinatorial optimizations

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Authors: Nicolas Zufferey

Abstract:

The vehicle routing problem (VRP) is a famous combinatorial optimization problem. Because of its well-known difficulty, metaheuristics are the most appropriate methods to tackle large and realistic instances. The goal of this paper is to highlight the key ideas for designing VRP metaheuristics according to the following criteria: efficiency, speed, robustness, and ability to take advantage of the problem structure. Such elements can obviously be used to build solution methods for other combinatorial optimization problems, at least in the deterministic field.

Keywords: Vehicle routing problem, Metaheuristics, Combinatorial optimization.

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Authors: Kourosh Parand, Zahra Delafkar, Fatemeh Baharifard

Abstract:

The problem of natural convection about a cone embedded in a porous medium at local Rayleigh numbers based on the boundary layer approximation and the Darcy-s law have been studied before. Similarity solutions for a full cone with the prescribed wall temperature or surface heat flux boundary conditions which is the power function of distance from the vertex of the inverted cone give us a third-order nonlinear differential equation. In this paper, an approximate method for solving higher-order ordinary differential equations is proposed. The approach is based on a rational Chebyshev Tau (RCT) method. The operational matrices of the derivative and product of rational Chebyshev (RC) functions are presented. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ordinary differential equations to the solution of a system of algebraic equations. We also present the comparison of this work with others and show that the present method is applicable.

Keywords: Tau method, semi-infinite, nonlinear ODE, rational Chebyshev, porous media.

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Authors: Mohammed Salem Alzahrani

Abstract:

In this paper the optimality of the solution of an existing real word assignment problem known as the seat assignment problem using Seat Assignment Method (SAM) is discussed. SAM is the newly driven method from three existing methods, Hungarian Method, Northwest Corner Method and Least Cost Method in a special way that produces the easiness & fairness among all methods that solve the seat assignment problem.

Keywords: Assignment Problem, Hungarian Method, Least Cost Method, Northwest Corner Method, Seat Assignment Method (SAM), A Real Word Assignment Problem.

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Authors: Mhand Hifi, Hedi Mhalla, Mustapha Michaphy

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In this paper, we study the multi-scenario knapsack problem, a variant of the well-known NP-Hard single knapsack problem. We investigate the use of an adaptive algorithm for solving heuristically the problem. The used method combines two complementary phases: a size reduction phase and a dynamic 2- opt procedure one. First, the reduction phase applies a polynomial reduction strategy; that is used for reducing the size problem. Second, the adaptive search procedure is applied in order to attain a feasible solution Finally, the performances of two versions of the proposed algorithm are evaluated on a set of randomly generated instances.

Keywords: combinatorial optimization, max-min optimization, knapsack, heuristics, problem reduction

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