After reviewing recent research in Graph Drawings, in this book, author investigated: 1) Novel heuristic algorithms to solve the 1-page and 2-page BCNPs. They obtained the results better than or comparable with existing algorithms. 2) Genetic algorithms for the BCNPs. They obtained better results than the latest heuristic algorithms. 3) Two neural network models for the 1-page and 2-page BCNPs, respectively, and the convergence of the neural network models. Both models obtained good results. Especially, the model for the 2-page BCNP achieved much better performance than the existing model. 4) The complexity of parallel genetic algorithms, and the unified framework of PGA models in the form of function PGA (subpopulation size, cluster size, migration period, topology). 5) Theorems about the 1-page and 2-page BCNs for some kinds of structural graphs. 6) Proximity to the optimal crossing numbers for the evaluation of different algorithms on some kinds of structural graphs, and conjectures of 1-page and 2-page BCNs for some kinds of structural graphs.
Graphs are known structures with many applications in various fields including computer science and information visualization. Drawing graphs makes understanding the meaning of graphs easy by geometrically representation of them. Many graph drawing algorithms have been presented in the literature. Most of them draw graphs on an unbounded surface. However, there are applications in which it is required to draw graphs on a prescribed size area. For example, consider a VLSI circuit which should be designed on a U-shaped PCB with prescribed size, or consider a software in which one would like to show a graph on a prescribed size area. In this book, we examine the complexity of this problem, and introduce new algorithms for drawing planar graphs on 2D surfaces which are bounded by simple polygons. The content of this book is suitable for use in advanced undergraduate and graduate level courses on algorithms, graph drawing, information visualization and computational geometry. The book will also serve as a useful reference for researchers and software developers in the field of graph drawing, information visualization, VLSI design and CAD.
In this monograph, we have designed some sequential algorithm to solve some problems on interval graphs, permutation graphs and trapezoid graphs. In chapter 1, we have discussed the definitions, recognitions, applications, survey, etc. of the Interval, permutation and trapezoid graphs. In second chapter we have designed an O(n) time algorithm to solve minimum k-neighbourhood-covering problem on interval graphs. We also present efficient algorithms to find next-to-shortest path between any pair of vertices on permutation graphs and trapezoid graphs with n vertices which run in O(n^2) time in chapter 3 and chapter 5 respectively. In chapter 4, we present an O(n^2) time algorithm to find a minimum 2-tuple dominating set on permutation graphs with n vertices. Also in chapter 6, we present an algorithm to find a tree 4-spanner on trapezoid graphs in O(n) time, and in chapter 7, an O(n^2) time algorithm is presented to find a tree 3-spanner on trapezoid graphs, where n is the number of vertices of the graph. Finally, chapter 8 contains some concluding remarks and scopes of further research on the problems that have been studied in the monograph.
This monogram presents some sequential and parallel algorithms on intersection graphs. The algorithms are designed to solve some problems on interval, permutation and circular arc graphs. These algorithms measure some parameters on intersection graphs.This monogram presents some sequential and parallel algorithms on intersection graphs. The algorithms are deigned to solve some problems on interval, permutation and circular arc graphs. These algorithms measure some parameters on intersection graphs.
This monogram considers certain sequential and parallel algorithms on interval graphs, permutation graphs and trapezoid graphs. These graphs arise quite naturally in real-world applications. I have tried to present a rigorous and coherent theory. Proofs are constructive and are streamlined as much as possible. I have directed much attention to the algorithmic aspects of every problem. Algorithms are expressed in a manner that will make their adaption to a particular programming language relatively easy. The complexity of every algorithm is analyzed so that some measure of its efficiency can be determined. This monogram will be very useful for applied mathematicians and computer scientists at the research level. Many applications of the theoretical and computational aspects of the subject are described throughout the monogram. The topics covered in this monogram have been chosen to fill a vacuum in the literature, and their interrelation.
Graph Theory is a subject in mathematics which has application to problems originating from different fields like engineering, economics, genetics, operation research,computer science,etc.This book entitled "SOME RECENT STUDIES IN GRAPH THEORY" deals with the study of some graph valued functions,its properties and characterization interms of crossing number one and forbidden subgraphs.The concept of Pathos is applied to acyclic graphs and new graph valued function called Pathos Line Graph and Pathos Lict Graph are defined and their properties are studied.The properties concentrated mainly are planarity,crossing number one,eulerian and hamiltonian.Using subdivision of a graph the second sequence lict graphs and lictact graphs are defined and these graphs are characterized.Finally,a new concept of Semimultiregular graphs is introduced and Semi Total Block Graphs are studied.This book enriches the knowledge of defining new graph valued functions.Extentions of the concept of Semimultiregular graphs may lead to many applicatons.This book is an ideal for academicians, young researchers in graph theory and can be a subject for the post graduate students in the universities and colleges.
The theme of this book is the spectral properties of graphs. The book is divided into four chapters. Chapter 1 presents some basic terminologies and notations. Chapter 2 devotes to hyperenergetic graphs and the largest eigenvalue of non-regular graphs associated with the spectrum of graphs. Chapter 3 provides some results on the Laplacian spectrum of graphs, included Laplacian spread, Laplacian spectral ratio, Laplacian-energy-like, Kirchhoff index and the sum of Laplacian eigenvalues. The separator, spread and spectral radius on signless Laplacian spectrum of graphs are studied in Chapter 4.
This book considres one the main problems in discrete mathematics which is called the classification problem. In such a problem, given a collection of properties, construct up to isomorphism all structures that satisfy them. In otherwords, the classification problem is the problem of determining complete systems of representatives of the isomorphism classes. Also, this book considers both the use of invariants and the use of partition backtracking for solving the isomorphism problems of 0,1-matrices, in general. It also discusses the inverse problem of finding all structures for a given invariant. This leads to the composition principle for incidence structures and eventually to some new results. The goal of this book is to be of great help to researchers. Also, it can be used for graduate courses in both mathematics and computer sciences.
MIVAR: Transition from Productions to Bipartite Graphs MIVAR Nets and Practical Realization of Automated Constructor of Algorithms Handling More than Three Million Production Rules. The theoretical transition from the graphs of production systems to the bipartite graphs of the MIVAR nets is shown. Examples of the implementation of the MIVAR nets in the formalisms of matrixes and graphs are given. The linear computational complexity of algorithms for automated building of objects and rules of the MIVAR nets is theoretically proved. On the basis of the MIVAR nets the UDAV software complex is developed, handling more than 1.17 million objects and more than 3.5 million rules on ordinary computers. The results of experiments that confirm a linear computational complexity of the MIVAR method of information processing are given.
The study of domination number in Cartesian products has received its main motivation from attempts to settle a conjecture made by V.G Vizing in 1968, where he conjectured that for any two graphs G and H, the product of the domination number of G and the domination number of H is a lower bound for the domination number of the Cartesian product of G and H. Most of the progress in settling this conjecture has been limited to verifying the conjectured lower bound if one of the graphs has some structural property. However, several authors have established various bounds for dominating the Cartesian product of any two graphs. It is the purpose of this book to present a comprehensive study on Vizing’s conjecture. Hopefully, this paves the way for the long-awaited proof for this outstanding conjecture. On the other hand, this book settles some previously open problems concerning the case when the conjectured bound is sharp. Some open problems, as well as a conjecture related to Vizing’s conjecture, are presented.
Random number generation is an important topic due to its applications in cryptography and simulation. There is a dearth of books exclusively dealing with the problem of random number generation. The problem of random number generation is broadly classified into true and pseudo random number generation. We present a good introduction to and critical review of the problem of pseudo random number generation(PRNG). We also include a novel algorithm Providence and its comparison with state of the art PRNG algorithms.
The book "Coluring of Cactus Graphs" is a combination of basic graph theory, different types graph colouring and algorithms to colour/label the graphs. L(h,k)-labelling is very powerful graph labelling in the field of radio communication system. In this book some L(h,k)-labelling problems have done for different values of h and k. Edge colouring and total labellings are also very impotant for solving some real life problems like GSM network, LAN connections etc. In this book the procedure of the above mentioned colourings and algorithms to colour/label the graphs are given. This is very unique book in graph colouring/labelling.
The query optimization problem has been widely addressed in Relational Database Management Systems (RDBMS). Many strategies have been implemented to solve this problem including deterministic algorithms, randomized algorithms, meta-heuristic algorithms and hybrid approaches. This book provides a literature review that includes solutions to the join-ordering problem using simulated annealing, genetic algorithms and ant colony optimization. Such methodologies deeply depend on the correct configuration of various input parameters. This book also introduces a new meta-heuristic approach based on the automata theory adapted to solve the join-ordering problem. The proposed method requires only a single input parameter that facilitates its usage respect to other methods. The algorithm was embedded into PostgreSQL and compared with the genetic competitor using random and star database schemas.
With the recent advances of data generation and acquisition systems and the success of several projects such as Human Genome, a large number of databases, especially in biological field are now available worldwide. The growing rate of such databases is also exponential. There is a need to explore and analyze such massive data to infer some inherent information. Clustering has been recognized as one of the widely used data mining techniques which is essential for data analysis to reveal natural structures and to identify interesting patterns in the underlying data. In the last decade, significant amount of research work has been carried out on cluster analysis and a large number of algorithms have been developed, particularly for biological data. Recently, much attention has been paid to develop various clustering algorithms based on neighborhood graphs such as minimum spanning tree (MST), Voronoi diagram and kd-trees. In this book, we mainly report on the hierarchical, partitional, density-based and graph-based clustering algorithms which are developed using such neighborhood graphs.
In this book we will consider two topics of the algebraic structures which concern the properties of finitely presented groups and semigroups. The first problem which we examine is the calculating of the Fibonacci length of two families of finitely presented groups. Also we get two applications of the Fibonaccilength on the classification of groups and graphs. These applications are theoretical results of this notion after all of its nice numerical results. The second problem which is investigated is a classification method for groups (the permutational property) which considered in 1987 by P. Longobradi and M.Maj. We mainly concentrate on the generalization of this property to the semigroups by using some combinatorial methods. Finally, we give GAP cod and present two programs that first calculate the Wall number of a given prime p and second Computes the order of finite semigroups.