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.

In this book some methods of Multi-objective Transportation Problem are discussed.This book contains seven chapters. Here,fuzzy approach is used to get the optimal solutions of Multi-objective Transportation problem. Also, the number of solved problems based on proposed algorithms has been discussed. The real life application is also used to check the feasibility of the propsed algorithms in this book.

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.

Generating random networks efficiently and accurately is an important challenge for practical applications, and an interesting question for theoretical study. This book presents and discusses common methods of generating random graphs. It begins with approaches such as Exponential Random Graph Models, where the targeted probability of each network appearing in the ensemble is specified. This section also includes degree-preserving randomisation algorithms, where the aim is to generate networks with the correct number of links at each node, and care must be taken to avoid introducing a bias. Separately, it looks at growth style algorithms (e.g. preferential attachment) which aim to model a real process and then to analyse the resulting ensemble of graphs. It also covers generating special types of graphs including modular graphs, graphs with community structure and temporal graphs.

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.

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 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.

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.

Structural alignment is the process of finding similarities between a pair of proteins based on their three-dimensional shape. Accurate detection of such similarities could reveal evolutionary relationships and predict the functions of different proteins. Despite the existing algorithms, the protein structure alignment problem is not completely solved. In this work a graph-theoretic approach is considered, which consists of representing tertiary protein structures as labeled graphs, and interpreting the structural alignment problem as a particular case of the Maximum Common Subgraph (MCS) problem. Our algorithm was then implemented under parallel platforms using a combination of threads and message passing techniques. Experiments were performed on a set of proteins selected randomly from the Protein Data Bank. The experiments proved the time- efficiency and accuracy of our method when compared to several other algorithms.

In mathematics and computer science, many systems of individuals and the relationships between them may be modeled as graphs. It is natural to consider the problem of graph exploration by an autonomous agent, e.g. an individual meeting members of a social network, a webcrawler exploring the web, optimizing protein folding by exploring the graph of allowable shapes, software moving on a network of computers, or the Mars rover exploring the terrain of Mars. This monograph compares numerous exploration algorithms, and introduces randomized versions of existing exploration algorithms including randomized rotor routers and the random basic walk. The question of recurrence vs. transience is settled for the random basic walk on the class of locally finite, bounded degree graphs, and this theory specializes to give bounds on the exploratory behavior of the random basic walk on finite graphs such as lattices and complete graphs. Applications, examples, and open problems are provided throughout the text.

This book entitled Studies on the Spectrum and the Energy of Graphs is a humble attempt at making a small addition to the vast ocean of results on the spectrum and energy of graphs in graph theory. We mention some very significant developments in the theory of eigenvalues and energy of graphs and also some recent results in the spectral theory of graphs. Some parts of the results mentioned in this book have been presented in international conferences and appeared in international scientific journals. The author is happy to share that the chapter on Reciprocal Graphs was presented in the ICM 2006 at Madrid.

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.

The book identifies 4 popular FDCT algorithms. Next it is mapped in a cluster architecture.The cluster specific parallel algorithm is written. The algorithms are analyzed through a timing diagram and the cluster utilization and time units taken to implement the algorithm is calculated.Proposed algorithm parallel DCT is introduced and explained.It is also mapped in the cluster architecture, cluster specific algorithm is written,timing diagram is constructed, and cluster utilization and time units taken is calculated.It is shown thorough graphs and tables that cluster utilization is highest and time units taken is lowest in parallelDCT. It is concluded that, in order to minimize the number of multiplications in popular FDCT algorithms cluster utilization is ignored. Whereas parallelDCT contains more number of multiplications but the cluster utilization is more and time unit is less. Hence the simple approach of parallelDCT is more effective.

## algorithms on the book crossing number problem of graphs в наличии / купить интернет-магазине

## Algorithms on the Book Crossing Number Problem of Graphs

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.

## Multi-Objective Transportation Problem

In this book some methods of Multi-objective Transportation Problem are discussed.This book contains seven chapters. Here,fuzzy approach is used to get the optimal solutions of Multi-objective Transportation problem. Also, the number of solved problems based on proposed algorithms has been discussed. The real life application is also used to check the feasibility of the propsed algorithms in this book.

## Some Algorithms on Intersection Graphs

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.

## Sequential and Parallel Algorithms on Intersection Graphs

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.

## Some Sequential and Parallel Algorithms

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.

## Generating Random Networks and Graphs

Generating random networks efficiently and accurately is an important challenge for practical applications, and an interesting question for theoretical study. This book presents and discusses common methods of generating random graphs. It begins with approaches such as Exponential Random Graph Models, where the targeted probability of each network appearing in the ensemble is specified. This section also includes degree-preserving randomisation algorithms, where the aim is to generate networks with the correct number of links at each node, and care must be taken to avoid introducing a bias. Separately, it looks at growth style algorithms (e.g. preferential attachment) which aim to model a real process and then to analyse the resulting ensemble of graphs. It also covers generating special types of graphs including modular graphs, graphs with community structure and temporal graphs.

## The Spectral Properties of Graphs

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.

## Colouring of Cactus Graphs

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.

## On the Domination Number of the Cartesian Product of Graphs

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.

## Олег Варламов Mivar NETs and logical inference with the linear complexity

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.

## Structural Alignment: A Graph-Theoretic Approach

Structural alignment is the process of finding similarities between a pair of proteins based on their three-dimensional shape. Accurate detection of such similarities could reveal evolutionary relationships and predict the functions of different proteins. Despite the existing algorithms, the protein structure alignment problem is not completely solved. In this work a graph-theoretic approach is considered, which consists of representing tertiary protein structures as labeled graphs, and interpreting the structural alignment problem as a particular case of the Maximum Common Subgraph (MCS) problem. Our algorithm was then implemented under parallel platforms using a combination of threads and message passing techniques. Experiments were performed on a set of proteins selected randomly from the Protein Data Bank. The experiments proved the time- efficiency and accuracy of our method when compared to several other algorithms.

## Traversals of Infinite Graphs with Random Local Orientations

In mathematics and computer science, many systems of individuals and the relationships between them may be modeled as graphs. It is natural to consider the problem of graph exploration by an autonomous agent, e.g. an individual meeting members of a social network, a webcrawler exploring the web, optimizing protein folding by exploring the graph of allowable shapes, software moving on a network of computers, or the Mars rover exploring the terrain of Mars. This monograph compares numerous exploration algorithms, and introduces randomized versions of existing exploration algorithms including randomized rotor routers and the random basic walk. The question of recurrence vs. transience is settled for the random basic walk on the class of locally finite, bounded degree graphs, and this theory specializes to give bounds on the exploratory behavior of the random basic walk on finite graphs such as lattices and complete graphs. Applications, examples, and open problems are provided throughout the text.

## Studies on the Spectrum and the Energy of Graphs

This book entitled Studies on the Spectrum and the Energy of Graphs is a humble attempt at making a small addition to the vast ocean of results on the spectrum and energy of graphs in graph theory. We mention some very significant developments in the theory of eigenvalues and energy of graphs and also some recent results in the spectral theory of graphs. Some parts of the results mentioned in this book have been presented in international conferences and appeared in international scientific journals. The author is happy to share that the chapter on Reciprocal Graphs was presented in the ICM 2006 at Madrid.

## Clustering Algorithms for Biological Data

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.

## Performance Analysis of FDCT Algorithms

The book identifies 4 popular FDCT algorithms. Next it is mapped in a cluster architecture.The cluster specific parallel algorithm is written. The algorithms are analyzed through a timing diagram and the cluster utilization and time units taken to implement the algorithm is calculated.Proposed algorithm parallel DCT is introduced and explained.It is also mapped in the cluster architecture, cluster specific algorithm is written,timing diagram is constructed, and cluster utilization and time units taken is calculated.It is shown thorough graphs and tables that cluster utilization is highest and time units taken is lowest in parallelDCT. It is concluded that, in order to minimize the number of multiplications in popular FDCT algorithms cluster utilization is ignored. Whereas parallelDCT contains more number of multiplications but the cluster utilization is more and time unit is less. Hence the simple approach of parallelDCT is more effective.