Book Description

This book examines results on transfinite graphs and networks achieved through research over the past several years. Two initial chapters present preliminary theory, summarizing all essential ideas needed. Subsequent chapters are devoted entirely to novel results and cover: Connectedness ideas and their relationship to hypergraphs • Distance ideas and their extension to transfinite graphs with more complications, such as the replacement of natural-number distances by ordinal-number distances • Nontransitivity of path-based connectedness alleviated by replacing paths with walks, leading to a more powerful theory for transfinite graphs and networks • The use of nonstandard analysis in novel ways that leads to several entirely new results concerning hyperreal operating points; this use of hyperreals encompasses for the first time transfinite networks and transmission lines containing inductances and capacitances, in addition to resistances. 

The book will appeal to diverse readers, including graduate students, electrical engineers, mathematicians, and physicists. Moreover, the growing and presently substantial number of mathematicians working in nonstandard analysis may well be attracted by the novel application of the analysis employed in the work.

Book Description

This is the third volume of a definitive work on coloured Petri nets. It contains a detailed presentation of 19 applications of CP-nets across a broad range of application areas, including a security system, ATM networks, audio/video systems, transaction processing, ISDN services, VLSI chips, document storage, distributed programming, electronic funds transfer, a naval vessel, chemical processing, nuclear waste management, and many more. Most of the projects were carried out in an industrial setting, and in each case the original authors have cooperated with the author and approved the new presentation. The author has taken care to unify the terminology and the CPN diagrams and to ensure that the background knowledge required has been provided in the first two volumes of the work. ... Read more

Reviews (4)

Integrate three volume to one
I feel that the writing style is a little confusing even though Jensen is a master. I also recommend to integrate the three volumes to one due to the simplicity and vol. 2 just took 182 pages. In addition, the notationsrelatively differ from the ones in Peterson's Petri nets.

Integrate three volume to one
I feel that the writing style is a little confusing even though Jensen is a master. I also recommend to integrate the three volumes to one due to the simplicity and vol. 2 just took 182 pages. In addition, the notationsrelatively differ from the ones in Peterson's Petri nets.

Integrate three volume to one
I feel that the writing style is a little confusing even though Jensen is a master. I also recommend to integrate the three volume to one due to the simplicity and vol. 2 just took 182 pages. In addition, the notationsrelatively differ from the ones in Peterson's Petri nets.

BEST BOOK FOR CPN
It is the best book of CPN for the people who intriest in Coloured Petri nets.And it is very helpful to the research fo CPN.Though I haven't owned this book,I wash Icould get it in the near day! ... Read more

Book Description

This book combines traditional graph theory with the matroid view of graphs in order to throw light on the mathematical approach to network analysis. The authors examine in detail two dual structures associated with a graph, namely circuits and cutsets. These are strongly dependent on one another and together constitute a third, hybrid, vertex-independent structure called a graphoid, whose study is here termed hybrid graph theory. This approach has particular relevance for network analysis. The first account of the subject in book form, the text includes many new results as well as the synthesizing and reworking of much research done over the past thirty years (historically, the study of hybrid aspects of graphs owes much to the foundational work of Japanese researchers). This work will be regarded as the definitive account of the subject, suitable for all working in theoretical network analysis: mathematicians, computer scientists or electrical engineers. ... Read more

Book Description

Reviews (6)

Let others vainly try t'immure The Circle in the Quadrature!
This book examines the ongoing (1655-1680) conflict between Thomas Hobbes and Oxford's Savilian Professor of Mathematics, John Wallis, over the squaring of the circle and related problems of Euclidian geometry. To the end of his long life, Hobbes asserted that he had succeeded in squaring the circle, and Wallis refuted him again and again. This "war" extended beyond mathematics, to, to each man's religious beliefs and politics.
What interested me most immediately was the cast: the people involved and their intellectual and personal relationships. Hobbes' first public involvement with squaring the circle, was his intervention in the dispute between the Danish mathematician Longoburg (Longomontanus) and John Pell. Interestingly, Hobbes demonstrated that Pell was correct in rejecting Longomontanus's claim to having squared the circle. Pell was author of an essay regarding establishment of a library of mathematical books and instruments. That essay was published as an appendix to his friend John Dury's The Reformed Librarian. Pell and Dury were part of the Hartlib circle, as was Theodor Haak, who reported Hobbes' role in the Pell/Longomontanus dispute to John Aubrey. After that we see Henry Oldenburg, secretary of the Royal Society, asking Hobbes to make up a list of mathematical texts. Presumably, the list was for Robert Boyle. In 1658 we find Thomas White and Kenelm Digby carrying communications between Fermat and Fenicle de Bessey in France and Lord Brouncker and Wallis in England. White, a Jesuit, had headed the English College at Douai; he had engaged Hobbes in debate over Galileo's Dialogues; and, at the end of a long life of intellectual distinction, he was caught up in the Popish Plot fabricated by Simon Oates. Etc.
It's worth describing the problem of squaring the circle, because it accounts for so much. Simply put: can a square be constructed that has the same area as a given circle, or vice versa? The key to the answer is in the word "constructed." By means of certain curves, such a square or circle can be defined. But those curves cannot be constructed using the classical instruments: ruler and compasses. Essentially, we're dealing with the transcendental character of pi, something that wasn't proved mathematically until the early 19th century.
Jesseph asks the question: why did Hobbes insist so long, to the end of his life, that he had squared the circle? Wallis refuted him again and again, but Hobbes hung on like a snapping turtle. Answering the question opens a window on the political, philosophical, social, and mathematical developments of the time. To summarize:
Hobbes's materialist philosophy brought him to support Isaac Barrow in Barrow's contention with Wallis over the primacy of geometry over arithmetic. These were the two components of classical mathematics, geometry dealing with continuous quantities and arithmetic with discrete. Barrow held that geometry was primary because it dealt with real physical reality, like distances and area, whereas numbers were abstractions: 1, 2, 3, etc. are concepts drawn from one egg, two brothers, three ships, and the like.
Hobbes' Erastianism--his contention in Leviathan that the king should be ruler over the religion of his subjects--placed him on the side of the Independents (congregationalists) against the Presbyterians in Protectorate religious politics. Hobbes, himself an atheist, felt that the Independents could be more easily be brought to heel by the King than the Presbyterians. Wallis was a Presbyterian, had even been Secretary of the Westminster Assembly.
Hobbes shared with the eduicational reformer John Webster and the Independent preacher William Dell a mistrust of the universities as temples to the scholasticism deriving from Aquinas. Wallis and his friend Seth Ward, Savilian Professor of Astronomy, were both actively involved in defending the universities from these attacks.
Of particular interest is the first of these issues. The debate between geometry and arithmetic came to the fore at this time because the distinction between the two was breaking down. Descartes (1637) and then Viete (1646) had defined analytical geometry. Napier (1620s?) had derived the logarithm from his work on the geometrical problem of the parallax. Cavalieri (1635) developed a "method of indivisibles": parallel slices of a geometric figure which, taken together, define the figure. Where this all is going, it seems to us in Whiggish hindsight, is toward notions of infinity, infinite series, and Newton's calculus.
I'll close by noting that Jesseph responds to Shapin and Schaffer, who, in their Leviathan and the Air-Pump, make "the success or failure of a scientific research program entirely independent of the truth or falsehood of the program's central claims." Jesseph calls their approach Wittgensteinian, but it was recognized when the book came out as post-modernist radicalism: science as pure social construct, without necessary basis in either the physical world or agreed canons of reason and method. The fact that Hobbes persisted so long in his claims is certainly less important than that after 1670 he was no longer taken seriously as a mathematician, except insofar as Wallis took the time and effort to refute him in the Transactions of the Royal Society.

Calvin(ism) and Hobbs
On the surface, this book seems an unlikely candidate for my enthusiasm. It appears to be 500 pages of minutia. In fact, the author starts out by saying it is an expansion of a footnote to an early work on the relatively obscure Calvinist mathematician Wallis. How perfectly academic! If that doesn't put the book out of reach, look forward to reading about 1000 footnotes.

Regardless, I think this a great book. Once I got comfortable with the terms, I realized this might be construed as something much more interesting than the traditional 'discovery' of mathematical truths. I'm still not exactly sure how to characterize it, but I'm having fun thinking it a history of science fiction. After all, 'squaring the circle' is the 17th century equivalent to predicting the winner of the Kentucky Derby or tomorrow's change in the Dow Jones Industrials. I may be stretching a bit here, but there is clearly more on the plate than justifying 17th century mathematic revolutions with apples falling on the head of a reclining Newton.

Rather than placing the subject matter in purely mathematical terms, Jesseph considers his material in a wider context, one that makes room for Restoration style science fiction. Keep in mind that Newton's alchemy was an early form of teleportation and the monads of Leibnitz took advantage of an early warp drive. Despite overtly humiliating Hobbs for his mathematical errors, its clear that Jesseph finds Hobbs the ultimate winner. Hobbs suffers no more from his lapse of academic rigor than any contemporary science fiction author. And like Jules Verne, the spirit of his ideas has won if not his details. The political science advocated by Hobbs in Leviathan is hard to distinguish from contemporary standards. Hobbs advocated severely limiting the legal authority of church bishops, scientific materialism and the notion that good laws could produce a good society. Meanwhile, Wallis would be known as a dogmatic right-wing Christian fundamentalist. Further, most of us are convinced that science has 'solved' the problem of 'squaring the circle' which is all Hobbs was advocating, anyway.

And so, Jesseph does a subtle job of indicting my modern sensibility. Painting Hobbs to be the fool, he is actually pointing a finger at my happy secular humanism. Bravo!

So, why is squaring the circle so tricky?

In short, an attempt to find the circle which is exactly 1 square foot in area forces us to confront conflicting intuitions about how we prove the existence of 'real' objects. Try it out for yourself. It is something you can attempt with pencil and paper, or better... try it with a home computer. One of the great things about this book is that it lays out the mathematical issues clearly enough that anyone with high school algebra and maybe an ability to write an excel spreadsheet, can play the 17th century geometer and mathematician. I had a great time doing a 'quadrature' in Excel. If you are interested, I'll email you the spreadsheet (see users.htcomp.net/markmills).

In summary, I think Jessup's book fits into a broad, ongoing reappraisal of mathematical history. I can identify 3 trends, 'Squaring the circle belonging to the 3rd and most important of them:

1. Bringing non-western mathematics to western readers. The best of this is the ongoing research into ancient Chinese mathematics. See 'Chinese Mathematics: A Concise History', Li Yan, Du Shiran, John N. Crossley, Anthony W.-C. Lun, Shih-Jan Tu or 'Astronomy and Mathematics in Ancient China: The Zhou Bi Suan Jing', Christopher Cullen. In short, most of what the Europeans called 'new' math in the 1500s had been around for 500 years in China.

2. Finding a physiological basis for mathematic intuitions. Check out the cognitive research described by 'Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being', George Lakoff, Rafael E. Nunez, Rafael Nuñez. All you really need to read is the first chapter. The rest is rather speculative.

3. Reappraising the conventional myths about heroic ancient European mathematicians. Unless your ambition is a tenured job teaching the history of math, you will have a great time reading sensible inquiries into pre-modern western math. Take a look at 'Biographies of Scientific Objects , Lorraine Daston (Editor), or Pappus of Alexandria and the Mathematics of Late Antiquity, Serafina Cuomo.

Hobbes and Wallis: a dispute that uncovers divergent concept
One cannot help wondering why two scholars did engage in such a fiercely dispute for half of their intellectual life. John Wallis, Oxford's Savilian professor of geometry had no trouble in exposing time and again the mathematical short-commings in the preposterous claims of so ill equiped an amateur mathematician as Thomas Hobbes. But why was the battle so intense and why should it cover nearly a quarter of a century, producing hundreds of letters, books and publications? Even more bewildering is the fact that the subject of the debate, squaring the circle, was later proved to be impossible and that neither the claims of Hobbes nor the rebuttals of Wallis contributed anything significant to the field of mathematics. Fortunately, Douglas Jesseph provides adequate answers to these questions in this excellent work on 17th century history of mathematics. A study of these important controversies sheds light on the reform of mathematics in the 17th century and exposes the widely divergent philosophical conceptions of mathematics to which both antagonists adhered.

A first fundamental issue concerned Hobbes' materialistic foundation of mathematics where Wallis reasoned from the traditional account that mathematical facts do not depend on the structure of the material world. A second source of dispute was the completely different concept of ratios: Wallis defended that those ratios could only be applied to homogoneous quantities. Thirdly, the angle of contact between a circle and its tangent was a subject of wilful misunderstanding from the part of Wallis. Finally, the important 17th-century debate on infinitesimal small quantities was heavily criticised by Hobbes and although he did not develop an alternative, his objections to some of the obscurities of Wallis' arithmetic of infinities were well justified. These disputed foundations on the philosophy of mathematics were not the only sources of the irreconcilable conflict. Wallis and Hobbes also held opposing views on methodological issues such as the nature of demonstration and the centuries-old discussion on analytic and synthetic methods. For Hobbes all demonstration must arise from causes and as such he rejected techniques from algebra and analytic geometry in which one starts by assuming the truth of the proposition that is ultimately sought and deduces consequences from that assumption. In doing so he tossed aside the tools that might have helped him in his desperate attempt to make his mark as mathematician. Apart from diverging views on the fundaments of mathematics and methodological issues, religious and political positions play part in explaining the controversy. Wallis fitted neatly into the reformed tradition while Hobbes' religious opinions stood far apart. Hobbes was excluded from the newly established Royal Society for ideological and personal reasons and as such was deprived from a forum to respond to his critics. His political opinions and his vitriolic polemics at universities brought him into conflict with many important people and explain at least some of the vehemence with which the dispute was conducted. However, Jesseph refrains from pursueing sociological reductionist account and spends part of the last chapter convincingly demonstrating the inadequacy of a purely sociological explanation of the dispute. By uncovering the conceptual gulf dividing Hobbes and Wallis, Jesseph succeeds in demonstrating important differences in the philosophy of mathematics in the 17th century and explains why these two men engaged in such ferocious fight. Objectively, Hobbes miserably failed attempt at the solution of classic geometric problems makes him the loser of this dispute. But one can feel in this book also some sympathy for the consequent way in which Hobbes rigorously applied principles of his philosophy to mathematics and ultimately rejected classical geometry to avoid an even worse fate: the refutation of his own philosophy.

Vitriolic, Invective, and Spleen: A 17th Century Dispute
The book is not, as I thought from the main title, centered on the mathematical issues. It is much more, and all the more enjoyable for providing the political, religious, and personal background to the dispute.

It was an exciting and perilous time, as the book is set against the background of the English Civil War, as men struggled to stay on the right side of first the monarchy, then Cromwell's protectorate, and then the monarchy again. This gives Jesseph's book a deep and rich texture, and adds drama to what could have been -- in a less capable writer's hands -- a dry discussion.

The last chapter brings in yet another aspect, as the author uses the Hobbes - Wallis debate to reflect into one of today's academic battles: Whether the results of science and mathematics are relative, that is, a product of sociological factors -- or if they have a standing that is independent of those factors. Jesseph's point of view is well-argued, and, for this reviewer, comes to the correct conclusion.

Poor Hobbes
Quite Good. Jesseph's well researched and well written book examines a famous episode in intellectual history and pronounces what must surely be the final word on the subject. Jesseph's scholarship is impressive (the footnotes contain much interesting collateral material), and he handles the technical aspects of his subject well. While Jesseph is strong on the social and political aspects of the "war" between Hobbes and Wallis, he clearly demonstrates that the vehemence of the dispute was attributable to Hobbes' colossal mathematical ineptitude and his equally colossal intransigence in refusing to acknowledge his crushing defeat. Whatever Hobbes' merits as a philosopher, his decades-long dispute with Wallis does him little credit. As a man of letters Hobbes perhaps retains some eminence; however any claim Hobbes may have as a serious thinker is fairly demolished by Wallis' savaging of Hobbes' mathematical pretensions, and Hobbes' increasingly desperate and ridiculous responses to this thrashing. Jesseph tells this story thoroughly and with wit. He even makes one feel a bit of compassion for Hobbes in his misguided and catastrophic foray into Euclid's realm. Well done. ... Read more

Book Description

Designed for the nonspecialist, this classic text by a world expert is an invaluable reference tool for those interested in a basic understanding of the subject. Exercises, notes and exhaustive references follow each chapter, making it outstanding as both a text and reference for students and researchers in graph theory and its applications. The reader will delight to discover that the topics in this book are coherently unified and include some of the deepest and most beautiful developments in graph theory. ... Read more

Book Description

In 1963 Oystein Ore wrote this classic volume, which was published in the New Mathematical Library Series. This elegant book has provided students and teachers with an excellent introduction to the field of graph theory for close to thirty years. Robin Wilson's revision adds strength to the book by updating the terminology and notation, bringing them in line with contemporary usage. Wilson has added new material on interval graphs, the traveling salesman problem, bracing frameworks, shortest route problems, and coloring maps on surfaces. Most of the diagrams in the book have been redrawn. ... Read more

Book Description

The application of graph theory to modelling systems began in several scientific areas, among them statistical physics (the study of large particle systems), genetics (studying inheritable properties of natural species), and interactions in contingency tables. The use of graphical models in statistics has increased considerably in these and other areas such as artificial intelligence, and the theory has been greatly developed and extended. This is the first comprehensive and authoritative account of the theory of graphical models. Written by a leading expert in the field, it contains the fundamentals graph required and a thorough study of Markov properties associated with various type of graphs, the statistical theory of log-linear and graphical models, and graphical tables with mixed discrete-continuous variables in developed detail. Special topics, such as the application of graphical models to probabilistic expert systems, are described briefly, and appendices give details of the multivariate normal distribution and of the theory of regular exponential families. ... Read more

Book Description

Group actions on trees furnish a unified geometric way of recasting the chapter of combinatorial group theory dealing with free groups, amalgams, and HNN extensions. Some of the principal examples arise from rank one simple Lie groups over a non-archimedean local field acting on their Bruhat--Tits trees. In particular this leads to a powerful method for studying lattices in such Lie groups. This monograph extends this approach to the more general investigation of $X$-lattices $\Gamma$, where $X$ is a locally finite tree and $\Gamma$ is a discrete group of automorphisms of $X$ of finite covolume. These "tree lattices" are the main object of study. Special attention is given to both parallels and contrasts with the case of Lie groups. Beyond the Lie group connection, the theory has applications to combinatorics and number theory. The authors present a coherent survey of the results on uniform tree lattices, and a (previously unpublished) development of the theory of non-uniform tree lattices, including some fundamental and recently proved existence theorems. Non-uniform tree lattices are much more complicated than unifrom ones; thus a good deal of attention is given to the construction and study of diverse examples. Some interesting new phenomena are observed here which cannot occur in the case of Lie groups. The fundamental technique is the encoding of tree actions in terms of the corresponding quotient "graph of groups." {\it Tree Lattices} should be a helpful resource to researchers in the field, and may also be used for a graduate course in geometric group theory. ... Read more

Reviews (1)

Affordable but not accurate
It's nice to have an affordable math book, and this one does give a good introduction to graph theory. Unfortunately, there are also mistakes (some of which REALLY should have been caught in proofreading) which could confuse someone attempting to learn graph theory from this book. (These are both in the text and in the answers provided for the problems, such as giving the wrong number for the length of a path) ... Read more

Book Description

The design of approximation algorithms for spanning tree problems has become an exciting and important area of theoretical computer science and also plays a significant role in emerging fields such as biological sequence alignments and evolutionary tree construction. While work in this field remains quite active, the time has come to collect under one cover spanning tree properties, classical results, and recent research developments.Spanning Trees and Optimization Problems offers the first complete treatment of spanning tree algorithms, from their role in classical computer science to their most modern applications. The authors first explain the general properties of spanning trees, then focus on three main categories: minimum spanning trees, shortest-paths trees, and minimum routing cost spanning trees. Along with the theoretical descriptions of the methods, numerous examples and applications illustrate the concepts in practice. The final chapter explores several other interesting spanning trees, including maximum leaf spanning trees, minimum diameter spanning trees, Steiner trees, and evolutionary trees.With logical organization, well chosen topics, and easy to understand pseudocode, the authors provide not only a full, rigorous treatment of theory and applications, but also an excellent handbook for spanning tree algorithms. This book will be a welcome addition to your reference shelf whether your interests lie in graph and approximation algorithms for theoretical work or you use graph techniques to solve practical problems ... Read more

Book Description

A timely convergence of two widely used disciplines

Random Graphs for Statistical Pattern Recognition is the first book to address the topic of random graphs as it applies to statistical pattern recognition. Both topics are of vital interest to researchers in various mathematical and statistical fields and have never before been treated together in one book. The use of data random graphs in pattern recognition in clusteringand classification is discussed, and the applications for both disciplines are enhanced with new tools for the statistical pattern recognition community. New and interesting applications for random graph users are also introduced.

This important addition to statistical literature features:

• Information that previously has been available only through scattered journal articles
• Practical tools and techniques for a wide range of real-world applications
• New perspectives on the relationship between pattern recognition and computational geometry
• Numerous experimental problems to encourage practical applications

With its comprehensive coverage of two timely fields, enhanced with many references and real-world examples, Random Graphs for Statistical Pattern Recognition is a valuable resource for industry professionals and students alike. ... Read more

Book Description

"Both authors are excellent expositors-exceptionally so-and this makes for a pleasurable read and allows for clear understanding of the mathematical concepts." -Joel Spencer Fractional Graph Theory explores the various ways in which integer-valued graph theory concepts can be modified to derive nonintegral values. Based on the authors' extensive review of the literature, it provides a unified treatment of the most important results in the study of fractional graph concepts. Professors Scheinerman and Ullman begin by developing a general fractional theory of hypergraphs and move on to provide in-depth coverage of fundamental and advanced topics, including fractional matching, fractional coloring, and fractional edge coloring; fractional arboricity via matroid methods; and fractional isomorphism. The final chapter is devoted to a variety of additional issues, such as fractional topological graph theory, fractional cycle double covers, fractional domination, fractional intersection number, and fractional aspects of partially ordered sets. Supplemented with many challenging exercises in each chapter as well as an abundance of references and bibliographic material, Fractional Graph Theory is a comprehensive reference for researchers and an excellent graduate-level text for students of graph theory and linear programming. ... Read more

Book Description

A unified, modern treatment of the theory of random graphs-including recent results and techniques
Since its inception in the 1960s, the theory of random graphs has evolved into a dynamic branch of discrete mathematics. Yet despite the lively activity and important applications, the last comprehensive volume on the subject is Bollobas's well-known 1985 book. Poised to stimulate research for years to come, this new work covers developments of the last decade, providing a much-needed, modern overview of this fast-growing area of combinatorics. Written by three highly respected members of the discrete mathematics community, the book incorporates many disparate results from across the literature, including results obtained by the authors and some completely new results. Current tools and techniques are also thoroughly emphasized. Clear, easily accessible presentations make Random Graphs an ideal introduction for newcomers to the field and an excellent reference for scientists interested in discrete mathematics and theoretical computer science. Special features include:
* A focus on the fundamental theory as well as basic models of random graphs
* A detailed description of the phase transition phenomenon
* Easy-to-apply exponential inequalities for large deviation bounds
* An extensive study of the problem of containing small subgraphs
* Results by Bollobas and others on the chromatic number of random graphs
* The result by Robinson and Wormald on the existence of Hamilton cycles in random regular graphs
* A gentle introduction to the zero-one laws
* Ample exercises, figures, and bibliographic references ... Read more

Book Description

This is a textbook on graph theory, especially suitable for computer scientists but also suitable for mathematicians with an interest in computational complexity. Although it introduces most of the classical concepts of pure and applied graph theory (spanning trees, connectivity, genus, colourability, flows in networks, matchings and traversals) and covers many of the major classical theorems, the emphasis is on algorithms and thier complexity: which graph problems have known efficient solutions and which are intractable. For the intractable problems a number of efficient approximation algorithms are included with known performance bounds. Informal use is made of a PASCAL-like programming language to describe the algorithms. A number of exercises and outlines of solutions are included to extend and motivate the material of the text. ... Read more

Book Description

This book focuses on the classic Steiner Problem and illustrates how results of the problem's development have generated the Theory of Minimal Networks, that is systems of "rubber" branching threads of minimal length. This theory demonstrates a brilliant interconnection among differential and computational geometry, topology, variational calculus, and graph theory. All necessary preliminary information is included, and the book's simplified format and nearly 150 illustrations and tables will help readers develop a concrete understanding of the material. All nontrivial statements are proved, and plenty of exercises are included. ... Read more

Book Description

A valuable resource for mathematics and computer science students, Graphs, Algorithms and Optimization presents the theory of graphs from an algorithmic viewpoint. The authors cover the key topics in graph theory and introduce discrete optimization and its connection to graph theory. The book contains a wealth of information on algorithms and the data structures needed to program them efficiently. Many programming techniques used for algorithms, algorithmic complexity and efficiency, a chapter on NP-completeness and three chapters on linear optimization are also included. The graph theory presented is rigorous, but the style is informal. ... Read more

Book Description

Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications focuses on discrete mathematics and combinatorial algorithms interacting with real world problems in computer science, operations research, applied mathematics and engineering. Its 11 chapters written by experts in their respective fields, and covers a wide spectrum of high-interest problems across these discipline domains. Among the contributing authors are Richard Karp of UC Berkeley and Robert Tarjan of Princeton; both are at the pinnacle of research scholarship in Graph Theory and Combinatorics. The chapters from the contributing authors focus on "real world" applications, all of which will be of considerable interest across the areas of Operations Research, Computer Science, Applied Mathematics, and Engineering. These problems include Internet congestion control, high-speed communication networks, multi-object auctions, resource allocation, software testing, data structures, etc. In sum, this is a book focused on major, contemporary problems, written by the top research scholars in the field, using cutting-edge mathematical and computational techniques.