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Classical computer science textbooks tell us that some problems are 'hard'. Yet many areas, from machine learning and computer vision to theorem proving and software verification, have defined their own set of tools for effectively solving complex problems. Tractability provides an overview of these different techniques, and of the fundamental concepts and properties used to tame intractability. This book will help you understand what to do when facing a hard computational problem. Can the problem be modelled by convex, or submodular functions? Will the instances arising in practice be of low treewidth, or exhibit another specific graph structure that makes them easy? Is it acceptable to use scalable, but approximate algorithms? A wide range of approaches is presented through self-contained chapters written by authoritative researchers on each topic. As a reference on a core problem in computer science, this book will appeal to theoreticians and practitioners alike.

Mathematics. --- Math --- Science --- Computer algorithms. --- Combinatorial optimization --- Computational complexity. --- Data processing. --- Algorithms --- Optimization, Combinatorial --- Combinatorial analysis --- Mathematical optimization --- Complexity, Computational --- Electronic data processing --- Machine theory

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The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily and completely rigorously to graduate students and advanced undergraduates. The book takes a number of specific problems and solves them, the needed tools developed along the way in the context of the particular problems. It treats a mélange of topics from combinatorial probability theory, number theory, random graph theory and combinatorics. The problems in this book involve the asymptotic analysis of a discrete construct as some natural parameter of the system tends to infinity. Besides bridging discrete mathematics and mathematical analysis, the book makes a modest attempt at bridging disciplines. The problems were selected with an eye toward accessibility to a wide audience, including advanced undergraduate students. The book could be used for a seminar course in which students present the lectures.

Mathematics. --- Number theory. --- Probabilities. --- Combinatorics. --- Graph theory. --- Probability Theory and Stochastic Processes. --- Graph Theory. --- Number Theory. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Combinatorics --- Algebra --- Mathematical analysis --- Number study --- Numbers, Theory of --- Combinatorial optimization. --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Extremal problems

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"Advances in Bio-inspired Combinatorial Optimization Problems" illustrates several recent bio-inspired efficient algorithms for solving NP-hard problems. Theoretical bio-inspired concepts and models, in particular for agents, ants and virtual robots are described. Large-scale optimization problems, for example: the Generalized Traveling Salesman Problem and the Railway Traveling Salesman Problem, are solved and their results are discussed. Some of the main concepts and models described in this book are: inner rule to guide ant search - a recent model in ant optimization, heterogeneous sensitive ants; virtual sensitive robots; ant-based techniques for static and dynamic routing problems; stigmergic collaborative agents and learning sensitive agents. This monograph is useful for researchers, students and all people interested in the recent natural computing frameworks. The reader is presumed to have knowledge of combinatorial optimization, graph theory, algorithms and programming. The book should furthermore allow readers to acquire ideas, concepts and models to use and develop new software for solving complex real-life problems.

Engineering & Applied Sciences --- Computer Science --- Biologically-inspired computing. --- Combinatorial optimization. --- Optimization, Combinatorial --- Biologically-inspired computing --- Bio-inspired computing --- Natural computing --- Engineering. --- Operations research. --- Decision making. --- Artificial intelligence. --- Computational intelligence. --- Computational Intelligence. --- Artificial Intelligence (incl. Robotics). --- Operation Research/Decision Theory. --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Construction --- Industrial arts --- Technology --- Decision making --- Combinatorial analysis --- Mathematical optimization --- Artificial Intelligence. --- Operations Research/Decision Theory.

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This book constitutes the refereed proceedings of the 8th International Conference on Combinatorial Optimization and Applications, COCOA 2014, held on the island of Maui, Hawaii, USA, in December 2014. The 56 full papers included in the book were carefully reviewed and selected from 133 submissions. Topics covered include classic combinatorial optimization; geometric optimization; network optimization; optimization in graphs; applied optimization; CSoNet; and complexity, cryptography, and games.

Computer science. --- Computer communication systems. --- Algorithms. --- Numerical analysis. --- Computer science --- Computer graphics. --- Computer Science. --- Algorithm Analysis and Problem Complexity. --- Discrete Mathematics in Computer Science. --- Numeric Computing. --- Computer Communication Networks. --- Computer Graphics. --- Mathematics. --- Computer software. --- Computational complexity. --- Electronic data processing. --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Software, Computer --- Computer systems --- Complexity, Computational --- Electronic data processing --- Machine theory --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Engineering graphics --- Image processing --- Algorism --- Algebra --- Arithmetic --- Automation --- Digital techniques --- Foundations --- Mathematical optimization --- Combinatorial optimization --- Mathematics --- Computer science—Mathematics. --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Network computers --- Mathematical analysis --- Distributed processing --- Discrete mathematics. --- Computer networks. --- Numerical Analysis. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis