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This book constitutes the proceedings of the 12th International Workshop on Algorithms and Models for the Web Graph, WAW 2015, held in Eindhoven, The Netherlands, in December 2015. The 15 full papers presented in this volume were carefully reviewed and selected from 24 submissions. They are organized in topical sections named: properties of large graph models, dynamic processes on large graphs, and properties of PageRank on large graphs.

This book constitutes the refereed proceedings of the 9th International Conference on Combinatorial Optimization and Applications, COCOA 2015, held in Houston, TX, USA, in December 2015. The 59 full papers included in the book were carefully reviewed and selected from 125 submissions. Topics covered include classic combinatorial optimization; geometric optimization; network optimization; applied optimization; complexity and game; and optimization in graphs.

This book constitutes the proceedings of the 12th International Conference on Latent Variable Analysis and Signal Separation, LVA/ICS 2015, held in Liberec, Czech Republic, in August 2015. The 61 revised full papers presented – 29 accepted as oral presentations and 32 accepted as poster presentations – were carefully reviewed and selected from numerous submissions. Five special topics are addressed: tensor-based methods for blind signal separation; deep neural networks for supervised speech separation/enhancement; joined analysis of multiple datasets, data fusion, and related topics; advances in nonlinear blind source separation; sparse and low rank modeling for acoustic signal processing.

This book constitutes the proceedings of the First International Conference on Codes, Cryptology and Information Security, C2SI 2015, held in Rabat, Morocco, in May 2015. The 22 regular papers presented together with 8 invited talks were carefully reviewed and selected from 59 submissions. The first aim of this conference is to pay homage to Thierry Berger for his valuable contribution in teaching and disseminating knowledge in coding theory and cryptography in Morocco since 2003. The second aim of the conference is to provide an international forum for researchers from academia and practitioners from industry from all over the world for discussion of all forms of cryptology, coding theory and information security.

This book collects the refereed proceedings of the First International Conference onon Algorithms and Discrete Applied Mathematics, CALDAM 2015, held in Kanpur, India, in February 2015. The volume contains 26 full revised papers from 58 submissions along with 2 invited talks presented at the conference. The workshop covered a diverse range of topics on algorithms and discrete mathematics, including computational geometry, algorithms including approximation algorithms, graph theory and computational complexity.

This book constitutes the proceedings of the 19th International Conference on Developments in Language Theory, DLT 2015, held in Liverpool, UK. The 31 papers presented together with 5 invited talks were carefully reviewed and selected from 54 submissions. Its scope is very general and includes, among others, the following topics and areas: combinatorial and algebraic properties of words and languages, grammars, acceptors and transducers for strings, trees, graphs, arrays, algebraic theories for automata and languages, codes, efficient text algorithms, symbolic dynamics, decision problems, relationships to complexity theory and logic, picture description and analysis, polyominoes and bidimensional patterns, cryptography, concurrency, cellular automata, bio-inspired computing, and quantum computing.

This book constitutes the proceedings of the 9th International Workshop on Frontiers in Algorithmics, FAW 2015, held in Guilin, China, in July 2015. The 28 papers presented in this volume were carefully reviewed and selected from 65 submissions. They deal with graph algorithms, approximation algorithms, combinatorial optimization, parameterized algorithms, and online algorithms.

This book constitutes the proceedings of the 10th International Computer Science Symposium in Russia, CSR 2015, held in Listvyanka, Russia, in July 2015.The 25 full papers presented in this volume were carefully reviewed and selected from 61 submissions. In addition the book contains 4 invited lectures. The scope of the proposed topics is quite broad and covers a wide range of areas in theoretical computer science and its applications.

This book constitutes the proceedings of the 15th IMA International Conference on Cryptography and Coding, IMACC 2015, held at Oxford, UK, in December 2015. The 18 papers presented together with 1 invited talk were carefully reviewed and selected from 36 submissions. The scope of the conference was on following topics: authentication, symmetric cryptography, 2-party computation, codes, Boolean functions, information theory, and leakage resilience.

This book constitutes the proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing, CASC 2015, held in Aachen, Germany, in September 2015. The 35 full papers presented in this volume were carefully reviewed and selected from 42 submissions. They deal with the ongoing progress both in theoretical computer algebra and its expanding applications. New and closer interactions are fostered by combining the area of computer algebra methods and systems and the application of the tools of computer algebra for the solution of problems in scientific computing.

This book constitutes the refereed proceedings of the 17th International Conference on Descriptional Complexity of Formal Systems, DCFS 2015, held in Waterloo, ON, Canada, in June 2015. The 23 full papers presented together with 2 invited talks were carefully reviewed and selected from 29 submissions. The subject of the workshop was descriptional complexity. Roughly speaking, this field is concerned with the size of objects in various mathematical models of computation, such as finite automata, pushdown automata, and Turing machines. Descriptional complexity serves as a theoretical representation of physical realizations, such as the engineering complexity of computer software and hardware. It also models similar complexity phenomena in other areas of computer science, including unconventional computing and bioinformatics.

This book constitutes the refereed proceedings of the 7th International Conference on Machines, Computations, and Universality, MCU 2015, held in Famagusta, North Cyprus, in September 2015. The 10 revised full papers presented together with 4 invited talks were carefully reviewed and selected from 23 submissions. MCU explores computation in the setting of various discrete models (Turing machines, register machines, cellular automata, tile assembly systems, rewriting systems, molecular computing models, neural models, etc.) and analog and hybrid models (BSS machines, infinite time cellular automata, real machines, quantum computing, etc.).

This book constitutes the refereed proceedings of the Second International Conference on Geometric Science of Information, GSI 2015, held in Palaiseau, France, in October 2015. The 80 full papers presented were carefully reviewed and selected from 110 submissions and are organized into the following thematic sessions: Dimension reduction on Riemannian manifolds; optimal transport; optimal transport and applications in imagery/statistics; shape space and diffeomorphic mappings; random geometry/homology; Hessian information geometry; topological forms and Information; information geometry optimization; information geometry in image analysis; divergence geometry; optimization on manifold; Lie groups and geometric mechanics/thermodynamics; computational information geometry; Lie groups: novel statistical and computational frontiers; geometry of time series and linear dynamical systems; and Bayesian and information geometry for inverse problems.

Discrete quantum walks are quantum analogues of classical random walks. They are an important tool in quantum computing and a number of algorithms can be viewed as discrete quantum walks, in particular Grover's search algorithm. These walks are constructed on an underlying graph, and so there is a relation between properties of walks and properties of the graph. This book studies the mathematical problems that arise from this connection, and the different classes of walks that arise. Written at a level suitable for graduate students in mathematics, the only prerequisites are linear algebra and basic graph theory; no prior knowledge of physics is required. The text serves as an introduction to this important and rapidly developing area for mathematicians and as a detailed reference for computer scientists and physicists working on quantum information theory.

This book focuses on the creative elements of algorithmic design by delving into the phases involved in algorithm creation. The conceptual underpinnings of this creative process are analogous to the invention and development of mathematical theorems that result in the induction of combinatorial algorithms. Numerous issue examples are included in the book. It is intended to enhance readers'problem-solving abilities by imparting a grasp of the fundamental ideas behind algorithmic design. This book summarizes the most widely used computer algorithms and provides a comprehensive overview of algorithms and data structures for searching, sorting, and graph processing. The algorithms presented in this book represent a body of knowledge that has developed over the previous five decades and has become critical not just for professional programmers and computer scientists, but also for all students interested in mathematics, data science, and engineering. The reader of this book is meant to get knowledge about known ways for successfully resolving difficulties. They will become acquainted with various cutting-edge data structures and novel methods for utilizing data structures to improve the efficacy of algorithms. Because the book is virtually self-contained, it may be used as a course book, reference book, or self-study resource.

Numerical Algorithmic Science and Engineering (NAS&E), or more compactly, Numerical Algorithmics, is the theoretical and empirical study and the practical implementation and application of algorithms for solving finite-dimensional problems of a numeric nature. The variables of such problems are either discrete-valued, or continuous over the reals, or, and as is often the case, a combination of the two, and they may or may not have an underlying network/graph structure. This re-emerging discipline of numerical algorithmics within computer science is the counterpart of the now well-established discipline of numerical analysis within mathematics, where the latter's emphasis is on infinite-dimensional, continuous numerical problems and their finite-dimensional, continuous approximates. A discussion of the underlying rationale for numerical algorithmics, its foundational models of computation, its organizational details, and its role, in conjunction with numerical analysis, in support of the modern modus operandi of scientific computing, or computational science & engineering, is the primary focus of this short monograph. It comprises six chapters, each with its own bibliography. Chapters 2, 3 and 6 present the book's primary content. Chapters 1, 4, and 5 are briefer, and they provide contextual material for the three primary chapters and smooth the transition between them. Mathematical formalism has been kept to a minimum, and, whenever possible, visual and verbal forms of presentation are employed and the discussion enlivened through the use of motivating quotations and illustrative examples. The reader is expected to have a working knowledge of the basics of computer science, an exposure to basic linear algebra and calculus (and perhaps some real analysis), and an understanding of elementary mathematical concepts such as convexity of sets and functions, networks and graphs, and so on. Although this book is not suitable for use as the principal textbook for a course on numerical algorithmics (NAS&E), it will be of value as a supplementary reference for a variety of courses. It can also serve as the primary text for a research seminar. And it can be recommended for self-study of the foundations and organization of NAS&E to graduate and advanced undergraduate students with sufficient mathematical maturity and a background in computing. When departments of computer science were first created within universities worldwide during the middle of the twentieth century, numerical analysis was an important part of the curriculum. Its role within the discipline of computer science has greatly diminished over time, if not vanished altogether, and specialists in that area are now to be found mainly within other fields, in particular, mathematics and the physical sciences. A central concern of this monograph is the regrettable, downward trajectory of numerical analysis within computer science and how it can be arrested and suitably reconstituted. Resorting to a biblical metaphor, numerical algorithmics (NAS&E) as envisioned herein is neither old wine in new bottles, nor new wine in old bottles, but rather this re-emerging discipline is a decantation of an age-old vintage that can hopefully find its proper place within the larger arena of computer science, and at what appears now to be an opportune time.

This book focuses on linear time eigenvalue location algorithms for graphs. This subject relates to spectral graph theory, a field that combines tools and concepts of linear algebra and combinatorics, with applications ranging from image processing and data analysis to molecular descriptors and random walks. It has attracted a lot of attention and has since emerged as an area on its own.Studies in spectral graph theory seek to determine properties of a graph through matrices associated with it. It turns out that eigenvalues and eigenvectors have surprisingly many connections with the structure of a graph. This book approaches this subject under the perspective of eigenvalue location algorithms. These are algorithms that, given a symmetric graph matrix M and a real interval I, return the number of eigenvalues of M that lie in I. Since the algorithms described here are typically very fast, they allow one to quickly approximate the value of any eigenvalue, which is a basic step in most applications of spectral graph theory. Moreover, these algorithms are convenient theoretical tools for proving bounds on eigenvalues and their multiplicities, which was quite useful to solve longstanding open problems in the area. This book brings these algorithms together, revealing how similar they are in spirit, and presents some of their main applications.This work can be of special interest to graduate students and researchers in spectral graph theory, and to any mathematician who wishes to know more about eigenvalues associated with graphs. It can also serve as a compact textbook for short courses on the topic.

The main aim of the book is to give a review of all relevant information regarding a well-known and important problem of Feedback Arc Set (FAS). This review naturally also includes a history of the problem, as well as specific algorithms. To this point such a work does not exist: There are sources where one can find incomplete and perhaps untrustworthy information. With this book, information about FAS can be found easily in one place: formulation, description, theoretical background, applications, algorithms etc. Such a compendium will be of help to people involved in research, but also to people that want to quickly acquaint themselves with the problem and need reliable information. Thus research, professional work and learning can proceed in a more streamlined and faster way.

This book A Guide to Graph Algorithms offers high-quality content in the research area of graph algorithms and explores the latest developments in graph algorithmics. The reader will gain a comprehensive understanding of how to use algorithms to explore graphs. It is a collection of texts that have proved to be trend setters and good examples of that. The book aims at providing the reader with a deep understanding of the structural properties of graphs that are useful for the design of efficient algorithms. These algorithms have applications in finite state machine modelling, social network theory, biology, and mathematics. The book contains many exercises, some up at present-day research-level. The exercises encourage the reader to discover new techniques by putting things in a clear perspective. A study of this book will provide the reader with many powerful tools to model and tackle problems in real-world scenarios.

This book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics. A focus on effective algorithms leads to the development of computer algebra software of use to researchers in these domains. After a survey of current results and open problems on decidability in enumerative combinatorics, the text shows how the cutting edge of this research is the new domain of Analytic Combinatorics in Several Variables (ACSV). The remaining chapters of the text alternate between a pedagogical development of the theory, applications (including the resolution by this author of conjectures in lattice path enumeration which resisted several other approaches), and the development of algorithms. The final chapters in the text show, through examples and general theory, how results from stratified Morse theorycan help refine some of these computability questions. Complementing the written presentation are over 50 worksheets for the SageMath and Maple computer algebra systems working through examples in the text.

This book is an extended and revised version of'Numerical Semigroups with Applications,'published by Springer as part of the RSME series. Like the first edition, it presents applications of numerical semigroups in Algebraic Geometry, Number Theory and Coding Theory. It starts by discussing the basic notions related to numerical semigroups and those needed to understand semigroups associated with irreducible meromorphic series. It then derives a series of applications in curves and factorization invariants. A new chapter is included, which offers a detailed review of ideals for numerical semigroups. Based on this new chapter, descriptions of the module of Kähler differentials for an algebroid curve and for a polynomial curve are provided. Moreover, the concept of tame degree has been included, and is viewed in relation to other factorization invariants appearing in the first edition. This content highlights new applications of numerical semigroups and their ideals, following in the spirit of the first edition.

This practically-focused study guide introduces the fundamentals of discrete mathematics through an extensive set of classroom-tested problems. Each chapter presents a concise introduction to the relevant theory, followed by a detailed account of common challenges and methods for overcoming these. The reader is then encouraged to practice solving such problems for themselves, by tackling a varied selection of questions and assignments of different levels of complexity.This updated second edition now covers the design and analysis of algorithms using Python, and features more than 50 new problems, complete with solutions.Topics and features: provides a substantial collection of problems and examples of varying levels of difficulty, suitable for both laboratory practical training and self-study; offers detailed solutions to each problem, applying commonly-used methods and computational schemes; introduces the fundamentals of mathematical logic, the theory of algorithms, Boolean algebra, graph theory, sets, relations, functions, and combinatorics; presents more advanced material on the design and analysis of algorithms, including Turing machines, asymptotic analysis, and parallel algorithms; includes reference lists of trigonometric and finite summation formulae in an appendix, together with basic rules for differential and integral calculus.This hands-on workbook is an invaluable resource for undergraduate students of computer science, informatics, and electronic engineering. Suitable for use in a one- or two-semester course on discrete mathematics, the text emphasizes the skills required to develop and implement an algorithm in a specific programming language.

This book constitutes the refereed proceedings of the 20th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2019, held in Ann Arbor, MI, USA, in May 2019. The 33 full versions of extended abstracts presented were carefully reviewed and selected from 114 submissions. The conference is a forum for researchers and practitioners working on various aspects of integer programming and combinatorial optimization. The aim is to present recent developments in theory, computation, and applications in these areas.

This work reviews the most important results regarding the use of the α-point in Scheduling Theory. It provides a number of different LP-relaxations for scheduling problems and seeks to explain their polyhedral consequences. It also explains the concept of the α-point and how the conversion algorithm works, pointing out the relations to the sum of the weighted completion times. Lastly, the book explores the latest techniques used for many scheduling problems with different constraints, such as release dates, precedences, and parallel machines. This reference book is intended for advanced undergraduate and postgraduate students who are interested in scheduling theory. It is also inspiring for researchers wanting to learn about sophisticated techniques and open problems of the field.

This practically-oriented textbook presents an accessible introduction to discrete mathematics through a substantial collection of classroom-tested exercises. Each chapter opens with concise coverage of the theory underlying the topic, reviewing the basic concepts and establishing the terminology, as well as providing the key formulae and instructions on their use. This is then followed by a detailed account of the most common problems in the area, before the reader is invited to practice solving such problems for themselves through a varied series of questions and assignments.Topics and features: provides an extensive set of exercises and examples of varying levels of complexity, suitable for both laboratory practical training and self-study; offers detailed solutions to many problems, applying commonly-used methods and computational schemes; introduces the fundamentals of mathematical logic, the theory of algorithms, Boolean algebra, graph theory, sets, relations, functions, and combinatorics; presents more advanced material on the design and analysis of algorithms, including asymptotic analysis, and parallel algorithms; includes reference lists of trigonometric and finite summation formulae in an appendix, together with basic rules for differential and integral calculus.This hands-on study guide is designed to address the core needs of undergraduate students training in computer science, informatics, and electronic engineering, emphasizing the skills required to develop and implement an algorithm in a specific programming language.

This clearly structured textbook/reference presents a detailed and comprehensive review of the fundamental principles of sequential graph algorithms, approaches for NP-hard graph problems, and approximation algorithms and heuristics for such problems. The work also provides a comparative analysis of sequential, parallel and distributed graph algorithms – including algorithms for big data – and an investigation into the conversion principles between the three algorithmic methods.Topics and features: presents a comprehensive analysis of sequential graph algorithms; offers a unifying view by examining the same graph problem from each of the three paradigms of sequential, parallel and distributed algorithms; describes methods for the conversion between sequential, parallel and distributed graph algorithms; surveys methods for the analysis of large graphs and complex network applications; includes full implementation details for the problems presented throughout the text; provides additional supporting material at an accompanying website.This practical guide to the design and analysis of graph algorithms is ideal for advanced and graduate students of computer science, electrical and electronic engineering, and bioinformatics. The material covered will also be of value to any researcher familiar with the basics of discrete mathematics, graph theory and algorithms.

This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several. Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work inreal life.

This textbook provides an accessible introduction to the rich and beautiful area of hyperplane arrangement theory, where discrete mathematics, in the form of combinatorics and arithmetic, meets continuous mathematics, in the form of the topology and Hodge theory of complex algebraic varieties.The topics discussed in this book range from elementary combinatorics and discrete geometry to more advanced material on mixed Hodge structures, logarithmic connections and Milnor fibrations. The author covers a lot of ground in a relatively short amount of space, with a focus on defining concepts carefully and giving proofs of theorems in detail where needed. Including a number of surprising results and tantalizing open problems, this timely book also serves to acquaint the reader with the rapidly expanding literature on the subject.Hyperplane Arrangements will be particularly useful to graduate students and researchers who are interested in algebraic geometry or algebraic topology. The book contains numerous exercises at the end of each chapter, making it suitable for courses as well as self-study.

Featuring up-to-date coverage of three topics lying at the intersection of combinatorics and commutative algebra, namely Koszul algebras, primary decompositions and subdivision operations in simplicial complexes, this book has its focus on computations.'Computations and Combinatorics in Commutative Algebra'has been written by experts in both theoretical and computational aspects of these three subjects and is aimed at a broad audience, from experienced researchers who want to have an easy but deep review of the topics covered to postgraduate students who need a quick introduction to the techniques. The computational treatment of the material, including plenty of examples and code, will be useful for a wide range of professionals interested in the connections between commutative algebra and combinatorics.

This is the first book that focuses on practical algorithms for polynomial inequality proving and discovering. It is a summary of the work by the authors and their collaborators on automated inequality proving and discovering in recent years. Besides brief introduction to some classical results and related work in corresponding chapters, the book mainly focuses on the algorithms initiated by the authors and their collaborators, such as real root counting, real root classification, improved CAD projection, dimension-decreasing algorithm, difference substitution, and so on. All the algorithms were rigorously proved and the implementations are demonstrated by lots of examples in various backgrounds such as algebra, geometry, biological science, and computer science.

Machine Learning: A Constraint-Based Approach provides readers with a refreshing look at the basic models and algorithms of machine learning, with an emphasis on current topics of interest that includes neural networks and kernel machines. The book presents the information in a truly unified manner that is based on the notion of learning from environmental constraints. While regarding symbolic knowledge bases as a collection of constraints, the book draws a path towards a deep integration with machine learning that relies on the idea of adopting multivalued logic formalisms, like in fuzzy systems. A special attention is reserved to deep learning, which nicely fits the constrained- based approach followed in this book. This book presents a simpler unified notion of regularization, which is strictly connected with the parsimony principle, and includes many solved exercises that are classified according to the Donald Knuth ranking of difficulty, which essentially consists of a mix of warm-up exercises that lead to deeper research problems. A software simulator is also included. Presents fundamental machine learning concepts, such as neural networks and kernel machines in a unified manner Provides in-depth coverage of unsupervised and semi-supervised learning Includes a software simulator for kernel machines and learning from constraints that also includes exercises to facilitate learning Contains 250 solved examples and exercises chosen particularly for their progression of difficulty from simple to complex

This treatise presents an integrated perspective on the interplay of set theory and graph theory, providing an extensive selection of examples that highlight how methods from one theory can be used to better solve problems originated in the other. Features: explores the interrelationships between sets and graphs and their applications to finite combinatorics; introduces the fundamental graph-theoretical notions from the standpoint of both set theory and dyadic logic, and presents a discussion on set universes; explains how sets can conveniently model graphs, discussing set graphs and set-theoretic representations of claw-free graphs; investigates when it is convenient to represent sets by graphs, covering counting and encoding problems, the random generation of sets, and the analysis of infinite sets; presents excerpts of formal proofs concerning graphs, whose correctness was verified by means of an automated proof-assistant; contains numerous exercises, examples, definitions, problemsand insight panels.

This book examines the problem of maintenance planning and scheduling in industrial production systems. It presents two practically relevant, deterministic mathematical models: the capacitated planned maintenance problem (CPMP) and the weighted uncapacitated planned maintenance problem (WUPMP). It introduces specific optimization algorithms such as construction heuristics, Lagrangean and tabu search metaheuristics. A problem independent hybrid approach links and alternates between two Lagrangean relaxations. It also analyzes the solvability with respect to the computational complexity of several problem classes, polyhedral properties and lower bounds. Computational studies demonstrate the performance of the heuristics, lower bounds, subgradients obtained from heuristics and the quality of dual information. This unique book includes implementation details and an introduction to the necessary theory making it suitable for upper undergraduate students.

Sebastian Goderbauer zeigt, dass das Einteilen von Wahlkreisen für die Deutsche Bundestagswahl aufgrund der gesetzlichen Vorgaben als ein mathematisches Optimierungsproblem angesehen werden kann. Er gibt eine detaillierte Komplexitätsanalyse des zugrundeliegenden Partitionsproblems an und untersucht, welches die beste Wahlkreisanzahl für Deutschland ist. Der Autor entwickelt einen optimierungsbasierten Algorithmus zum Einteilen von Wahlkreisen und wendet diesen auf deutsche Bevölkerungsdaten an.

The book is based on the PhD thesis “Descriptive Set Theoretic Methods in Automata Theory,” awarded the E.W. Beth Prize in 2015 for outstanding dissertations in the fields of logic, language, and information. The thesis reveals unexpected connections between advanced concepts in logic, descriptive set theory, topology, and automata theory and provides many deep insights into the interplay between these fields. It opens new perspectives on central problems in the theory of automata on infinite words and trees and offers very impressive advances in this theory from the point of view of topology.'…the thesis of Michał Skrzypczak offers certainly what we expect from excellent mathematics: new unexpected connections between a priori distinct concepts, and proofs involving enlightening ideas.” Thomas Colcombet.

Algorithm Engineering is a methodology for algorithmic research that combines theory with implementation and experimentation in order to obtain better algorithms with high practical impact. Traditionally, the study of algorithms was dominated by mathematical (worst-case) analysis. In Algorithm Engineering, algorithms are also implemented and experiments conducted in a systematic way, sometimes resembling the experimentation processes known from fields such as biology, chemistry, or physics. This helps in counteracting an otherwise growing gap between theory and practice.

This book explores fundamental aspects of geometric network optimisation with applications to a variety of real world problems. It presents, for the first time in the literature, a cohesive mathematical framework within which the properties of such optimal interconnection networks can be understood across a wide range of metrics and cost functions. The book makes use of this mathematical theory to develop efficient algorithms for constructing such networks, with an emphasis on exact solutions.Marcus Brazil and Martin Zachariasen focus principally on the geometric structure of optimal interconnection networks, also known as Steiner trees, in the plane. They show readers how an understanding of this structure can lead to practical exact algorithms for constructing such trees. The book also details numerous breakthroughs in this area over the past 20 years, features clearly written proofs, and is supported by 135 colour and 15 black and white figures. It will help graduate students, working mathematicians, engineers and computer scientists to understand the principles required for designing interconnection networks in the plane that are as cost efficient as possible.