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213 results in Algorithmics, Complexity, Computer Algebra, Computational Geometry

Page 1 of 11

Quantum Computing for Programmers
  • 2nd edition
  • Robert Hundt
  • Coming soon
  • Expected online publication date:
    November 2025
    Print publication:
    30 November 2025

Syntax and Semantics of Petri Nets
  • Roberto Gorrieri
  • Coming soon
  • Expected online publication date:
    August 2025
    Print publication:
    31 August 2025
  • Petri nets are one of the most popular tools for modeling distributed systems. This book provides a modern look at the theory behind them, by studying three classes of nets that model (i) sequential systems, (ii) non-communicating parallel systems, and (iii) communicating parallel systems. A decidable and causality respecting behavioral equivalence is presented for each class, followed by a modal logic characterization for each equivalence. The author then introduces a suitable process algebra for the corresponding class of nets and proves that the behavioral equivalence proposed for each class is a congruence for the operator of the corresponding process algebra. Finally, an axiomatization of the behavioral congruence is proposed. The theory is introduced step by step, with ordinary-language explanations and examples provided throughout, to remain accessible to readers without specialized training in concurrency theory or formal logic. Exercises with solutions solidify understanding, and the final chapter hints at extensions of the theory.

Proof Complexity Generators
  • Jan Krajíček
  • Coming soon
  • Expected online publication date:
    June 2025
    Print publication:
    31 May 2025
  • The P vs. NP problem is one of the fundamental problems of mathematics. It asks whether propositional tautologies can be recognized by a polynomial-time algorithm. The problem would be solved in the negative if one could show that there are propositional tautologies that are very hard to prove, no matter how powerful the proof system you use. This is the foundational problem (the NP vs. coNP problem) of proof complexity, an area linking mathematical logic and computational complexity theory. Written by a leading expert in the field, this book presents a theory for constructing such hard tautologies. It introduces the theory step by step, starting with the historic background and a motivational problem in bounded arithmetic, before taking the reader on a tour of various vistas of the field. Finally, it formulates several research problems to highlight new avenues of research.

Data Structures and Algorithms Using Python
  • Subrata Saha
  • Coming soon
  • Expected online publication date:
    April 2025
    Print publication:
    15 June 2023
  • Efficiently using data structures to collect, organise and retrieve information is one of the core abilities modern computer engineers are expected to have. This student-friendly textbook provides a complete view of data structures and algorithms using the Python programming language, striking a balance between theory and practical application. All major algorithms have been discussed and analysed in detail, and the corresponding codes in Python have been provided. Diagrams and examples have been extensively used for better understanding. Running time complexities are also discussed for each algorithm, allowing the student to better understand how to select the appropriate one. Written with both undergraduate and graduate students in mind, the book will also be helpful with competitive examinations for engineering in India such as GATE and NET. As such, it will be a vital resource for students as well as professionals who are looking for a handbook on data structures in Python.

Quantum Algorithms
  • A Survey of Applications and End-to-end Complexities
  • Alexander M. Dalzell, Sam McArdle, Mario Berta, Przemyslaw Bienias, Chi-Fang Chen, András Gilyén, Connor T. Hann, Michael J. Kastoryano, Emil T. Khabiboulline, Aleksander Kubica, Grant Salton, Samson Wang, Fernando G. S. L. Brandão
  • Coming soon
  • Expected online publication date:
    April 2025
    Print publication:
    24 April 2025
  • The 1994 discovery of Shor's quantum algorithm for integer factorization—an important practical problem in the area of cryptography—demonstrated quantum computing's potential for real-world impact. Since then, researchers have worked intensively to expand the list of practical problems that quantum algorithms can solve effectively. This book surveys the fruits of this effort, covering proposed quantum algorithms for concrete problems in many application areas, including quantum chemistry, optimization, finance, and machine learning. For each quantum algorithm considered, the book clearly states the problem being solved and the full computational complexity of the procedure, making sure to account for the contribution from all the underlying primitive ingredients. Separately, the book provides a detailed, independent summary of the most common algorithmic primitives. It has a modular, encyclopedic format to facilitate navigation of the material and to provide a quick reference for designers of quantum algorithms and quantum computing researchers.

Oriented Matroids
  • Laura Anderson
  • Coming soon
  • Expected online publication date:
    April 2025
    Print publication:
    10 April 2025
  • Oriented matroids appear throughout discrete geometry, with applications in algebra, topology, physics, and data analysis. This introduction to oriented matroids is intended for graduate students, scientists wanting to apply oriented matroids, and researchers in pure mathematics. The presentation is geometrically motivated and largely self-contained, and no knowledge of matroid theory is assumed. Beginning with geometric motivation grounded in linear algebra, the first chapters prove the major cryptomorphisms and the Topological Representation Theorem. From there the book uses basic topology to go directly from geometric intuition to rigorous discussion, avoiding the need for wider background knowledge. Topics include strong and weak maps, localizations and extensions, the Euclidean property and non-Euclidean properties, the Universality Theorem, convex polytopes, and triangulations. Themes that run throughout include the interplay between combinatorics, geometry, and topology, and the idea of oriented matroids as analogs to vector spaces over the real numbers and how this analogy plays out topologically.

Initial Algebras and Terminal Coalgebras
  • The Theory of Fixed Points of Functors
  • Jiří Adámek, Stefan Milius, Lawrence S. Moss
  • Published online:
    30 January 2025
    Print publication:
    06 February 2025
  • Providing an in-depth treatment of an exciting research area, this text's central topics are initial algebras and terminal coalgebras, primary objects of study in all areas of theoretical computer science connected to semantics. It contains a thorough presentation of iterative constructions, giving both classical and new results on terminal coalgebras obtained by limits of canonical chains, and initial algebras obtained by colimits. These constructions are also developed in enriched settings, especially those enriched over complete partial orders and complete metric spaces, connecting the book to topics like domain theory. Also included are an extensive treatment of set functors, and the first book-length presentation of the rational fixed point of a functor, and of lifting results which connect fixed points of set functors with fixed points of endofunctors on other categories. Representing more than fifteen years of work, this will be the leading text on the subject for years to come.

Data Structures and Algorithms in Java
  • A Project-Based Approach
  • Dan S. Myers
  • Published online:
    19 December 2024
    Print publication:
    31 October 2024
  • Learn with confidence with this hands-on undergraduate textbook for CS2 courses. Active-learning and real-world projects underpin each chapter, briefly reviewing programming fundamentals then progressing to core data structures and algorithms topics including recursion, lists, stacks, trees, graphs, sorting, and complexity analysis. Creative projects and applications put theoretical concepts into practice, helping students master the fundamentals. Dedicated project chapters supply further programming practice using real-world, interdisciplinary problems which students can showcase in their own online portfolios. Example Interview Questions sections prepare students for job applications. The pedagogy supports self-directed and skills-based learning with over 250 'Try It Yourself' boxes, many with solutions provided, and over 500 progressively challenging end-of-chapter questions. Written in a clear and engaging style, this textbook is a complete resource for teaching the fundamental skills that today's students need. Instructor resources are available online, including a test bank, solutions manual, and sample code.

Approximation Algorithms for Traveling Salesman Problems
  • Vera Traub, Jens Vygen
  • Published online:
    14 November 2024
    Print publication:
    05 December 2024
  • The Traveling Salesman Problem (TSP) is a central topic in discrete mathematics and theoretical computer science. It has been one of the driving forces in combinatorial optimization. The design and analysis of better and better approximation algorithms for the TSP has proved challenging but very fruitful. This is the first book on approximation algorithms for the TSP, featuring a comprehensive collection of all major results and an overview of the most intriguing open problems. Many of the presented results have been discovered only recently, and some are published here for the first time, including better approximation algorithms for the asymmetric TSP and its path version. This book constitutes and advances the state of the art and makes it accessible to a wider audience. Featuring detailed proofs, over 170 exercises, and 100 color figures, this book is an excellent resource for teaching, self-study, and further research.

How to Think about Algorithms
  • 2nd edition
  • Jeff Edmonds
  • Published online:
    10 October 2024
    Print publication:
    07 March 2024
  • Understand algorithms and their design with this revised student-friendly textbook. Unlike other algorithms books, this one is approachable, the methods it explains are straightforward, and the insights it provides are numerous and valuable. Without grinding through lots of formal proof, students will benefit from step-by-step methods for developing algorithms, expert guidance on common pitfalls, and an appreciation of the bigger picture. Revised and updated, this second edition includes a new chapter on machine learning algorithms, and concise key concept summaries at the end of each part for quick reference. Also new to this edition are more than 150 new exercises: selected solutions are included to let students check their progress, while a full solutions manual is available online for instructors. No other text explains complex topics such as loop invariants as clearly, helping students to think abstractly and preparing them for creating their own innovative ways to solve problems.

Online Algorithms
  • Rahul Vaze
  • Published online:
    07 May 2024
    Print publication:
    16 November 2023
  • Online algorithms are a rich area of research with widespread applications in scheduling, combinatorial optimization, and resource allocation problems. This lucid textbook provides an easy but rigorous introduction to online algorithms for graduate and senior undergraduate students. In-depth coverage of most of the important topics is presented with special emphasis on elegant analysis. The book starts with classical online paradigms like the ski-rental, paging, list-accessing, bin packing, where performance of online algorithms is studied under the worst-case input and moves on to newer paradigms like 'beyond worst case', where online algorithms are augmented with predictions using machine learning algorithms. The book goes on to cover multiple applied problems such as routing in communication networks, server provisioning in cloud systems, communication with energy harvested from renewable sources, and sub-modular partitioning. Finally, a wide range of solved examples and practice exercises are included, allowing hands-on exposure to the concepts.

Polytopes and Graphs
  • Guillermo Pineda Villavicencio
  • Published online:
    14 March 2024
    Print publication:
    21 March 2024
  • This book introduces convex polytopes and their graphs, alongside the results and methodologies required to study them. It guides the reader from the basics to current research, presenting many open problems to facilitate the transition. The book includes results not previously found in other books, such as: the edge connectivity and linkedness of graphs of polytopes; the characterisation of their cycle space; the Minkowski decomposition of polytopes from the perspective of geometric graphs; Lei Xue's recent lower bound theorem on the number of faces of polytopes with a small number of vertices; and Gil Kalai's rigidity proof of the lower bound theorem for simplicial polytopes. This accessible introduction covers prerequisites from linear algebra, graph theory, and polytope theory. Each chapter concludes with exercises of varying difficulty, designed to help the reader engage with new concepts. These features make the book ideal for students and researchers new to the field.

Proven Impossible
  • Elementary Proofs of Profound Impossibility from Arrow, Bell, Chaitin, Gödel, Turing and More
  • Dan Gusfield
  • Published online:
    18 February 2024
    Print publication:
    18 January 2024
  • In mathematics, it simply is not true that 'you can't prove a negative'. Many revolutionary impossibility theorems reveal profound properties of logic, computation, fairness and the universe, and form the mathematical background of new technologies and Nobel prizes. But to fully appreciate these theorems and their impact on mathematics and beyond, you must understand their proofs.This book is the first to present these proofs for a broad, lay audience. It fully develops the simplest rigorous proofs found in the literature, reworked to contain less jargon and notation, and more background, intuition, examples, explanations, and exercises. Amazingly, all of the proofs in this book involve only arithmetic and basic logic – and are elementary, starting only from first principles and definitions. Very little background knowledge is required, and no specialized mathematical training – all you need is the discipline to follow logical arguments and a pen in your hand.

Topological Duality for Distributive Lattices
  • Theory and Applications
  • Mai Gehrke, Sam van Gool
  • Published online:
    16 February 2024
    Print publication:
    07 March 2024
  • Introducing Stone–Priestley duality theory and its applications to logic and theoretical computer science, this book equips graduate students and researchers with the theoretical background necessary for reading and understanding current research in the area. After giving a thorough introduction to the algebraic, topological, logical, and categorical aspects of the theory, the book covers two advanced applications in computer science, namely in domain theory and automata theory. These topics are at the forefront of active research seeking to unify semantic methods with more algorithmic topics in finite model theory. Frequent exercises punctuate the text, with hints and references provided.

Analytic Combinatorics in Several Variables
  • 2nd edition
  • Robin Pemantle, Mark C. Wilson, Stephen Melczer
  • Published online:
    08 February 2024
    Print publication:
    15 February 2024
  • Discrete structures model a vast array of objects ranging from DNA sequences to internet networks. The theory of generating functions provides an algebraic framework for discrete structures to be enumerated using mathematical tools. This book is the result of 25 years of work developing analytic machinery to recover asymptotics of multivariate sequences from their generating functions, using multivariate methods that rely on a combination of analytic, algebraic, and topological tools. The resulting theory of analytic combinatorics in several variables is put to use in diverse applications from mathematics, combinatorics, computer science, and the natural sciences. This new edition is even more accessible to graduate students, with many more exercises, computational examples with Sage worksheets to illustrate the main results, updated background material, additional illustrations, and a new chapter providing a conceptual overview.

Random Graphs and Complex Networks
  • Volume 2
  • Remco van der Hofstad
  • Published online:
    08 February 2024
    Print publication:
    08 February 2024
  • Complex networks are key to describing the connected nature of the society that we live in. This book, the second of two volumes, describes the local structure of random graph models for real-world networks and determines when these models have a giant component and when they are small-, and ultra-small, worlds. This is the first book to cover the theory and implications of local convergence, a crucial technique in the analysis of sparse random graphs. Suitable as a resource for researchers and PhD-level courses, it uses examples of real-world networks, such as the Internet and citation networks, as motivation for the models that are discussed, and includes exercises at the end of each chapter to develop intuition. The book closes with an extensive discussion of related models and problems that demonstratemodern approaches to network theory, such as community structure and directed models.

Modern Discrete Probability
  • An Essential Toolkit
  • Sébastien Roch
  • Published online:
    14 December 2023
    Print publication:
    18 January 2024
  • Providing a graduate-level introduction to discrete probability and its applications, this book develops a toolkit of essential techniques for analysing stochastic processes on graphs, other random discrete structures, and algorithms. Topics covered include the first and second moment methods, concentration inequalities, coupling and stochastic domination, martingales and potential theory, spectral methods, and branching processes. Each chapter expands on a fundamental technique, outlining common uses and showing them in action on simple examples and more substantial classical results. The focus is predominantly on non-asymptotic methods and results. All chapters provide a detailed background review section, plus exercises and signposts to the wider literature. Readers are assumed to have undergraduate-level linear algebra and basic real analysis, while prior exposure to graduate-level probability is recommended. This much-needed broad overview of discrete probability could serve as a textbook or as a reference for researchers in mathematics, statistics, data science, computer science and engineering.

Introduction to Probability for Computing
  • Mor Harchol-Balter
  • Published online:
    12 September 2023
    Print publication:
    28 September 2023
  • Learn about probability as it is used in computer science with this rigorous, yet highly accessible, undergraduate textbook. Fundamental probability concepts are explained in depth, prerequisite mathematics is summarized, and a wide range of computer science applications is described. Throughout, the material is presented in a “question and answer” style designed to encourage student engagement and understanding. Replete with almost 400 exercises, real-world computer science examples, and covering a wide range of topics from simulation with computer science workloads, to statistical inference, to randomized algorithms, to Markov models and queues, this interactive text is an invaluable learning tool whether your course covers probability with statistics, with stochastic processes, with randomized algorithms, or with simulation. The teaching package includes solutions, lecture slides, and lecture notes for students.

Graph Spectra for Complex Networks
  • 2nd edition
  • Piet Van Mieghem
  • Published online:
    07 September 2023
    Print publication:
    21 September 2023
  • This concise and self-contained introduction builds up the spectral theory of graphs from scratch, with linear algebra and the theory of polynomials developed in the later parts. The book focuses on properties and bounds for the eigenvalues of the adjacency, Laplacian and effective resistance matrices of a graph. The goal of the book is to collect spectral properties that may help to understand the behavior or main characteristics of real-world networks. The chapter on spectra of complex networks illustrates how the theory may be applied to deduce insights into real-world networks. The second edition contains new chapters on topics in linear algebra and on the effective resistance matrix, and treats the pseudoinverse of the Laplacian. The latter two matrices and the Laplacian describe linear processes, such as the flow of current, on a graph. The concepts of spectral sparsification and graph neural networks are included.

Graph Theory and Additive Combinatorics
  • Exploring Structure and Randomness
  • Yufei Zhao
  • Published online:
    10 August 2023
    Print publication:
    31 August 2023
  • Using the dichotomy of structure and pseudorandomness as a central theme, this accessible text provides a modern introduction to extremal graph theory and additive combinatorics. Readers will explore central results in additive combinatorics-notably the cornerstone theorems of Roth, Szemerédi, Freiman, and Green-Tao-and will gain additional insights into these ideas through graph theoretic perspectives. Topics discussed include the Turán problem, Szemerédi's graph regularity method, pseudorandom graphs, graph limits, graph homomorphism inequalities, Fourier analysis in additive combinatorics, the structure of set addition, and the sum-product problem. Important combinatorial, graph theoretic, analytic, Fourier, algebraic, and geometric methods are highlighted. Students will appreciate the chapter summaries, many figures and exercises, and freely available lecture videos on MIT OpenCourseWare. Meant as an introduction for students and researchers studying combinatorics, theoretical computer science, analysis, probability, and number theory, the text assumes only basic familiarity with abstract algebra, analysis, and linear algebra.

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