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Combinatorial optimization. --- Mathematical optimization. --- Optimisation combinatoire --- Optimisation mathématique --- Computer algorithms --- Online algorithms --- Combinatorial optimization --- Computer Science --- Engineering & Applied Sciences --- Data processing --- Computer algorithms. --- Online algorithms. --- Data processing. --- Optimization, Combinatorial --- 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. --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- Computer mathematics --- Discrete mathematics --- Mathematical analysis --- Algorism --- Algebra --- Arithmetic --- 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 --- Informatics --- Science --- Digital techniques --- Mathematics --- Foundations --- Distributed processing --- Combinatorial analysis --- Mathematical optimization --- Online data processing --- Algorithms --- Computer software. --- Computational complexity. --- Electronic data processing. --- ADP (Data processing) --- Automatic data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Complexity, Computational --- Machine theory --- Software, Computer --- Computer systems --- Automation --- Computer science—Mathematics. --- Discrete mathematics. --- Computer networks. --- Numerical Analysis. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis
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Complex analysis --- Discrete mathematics --- Computer science --- Computer architecture. Operating systems --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- discrete wiskunde --- complexe analyse (wiskunde) --- grafische vormgeving --- informatica --- algoritmen --- KI (kunstmatige intelligentie) --- computernetwerken --- numerieke analyse --- AI (artificiële intelligentie)
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In this book, we present some recent advances in the ?eld of combinatorial optimization focusing on the design of e?cient approximation and on-line - gorithms. Combinatorial optimization and polynomial time approximation are verycloselyrelated:givenanNP-hardcombinatorialoptimizationproblem,i. e. , a problem for which no polynomial time algorithm exists unlessP =NP,one important approach used by computer scientists is to consider polynomial time algorithms that do not produce optimum solutions, but solutions that are pr- ably close to the optimum. A natural partition of combinatorial optimization problems into two classes is then of both practical and theoretical interest: the problemsthat arefully approximable, i. e. , thoseforwhich thereis anapproxi- tion algorithm that can approach the optimum with any arbitrary precision in terms of relative error and the problems that are partly approximable, i. e. , those for which it is possible to approach the optimum only until a ?xed factor unless P =NP. For some of these problems, especially those that are motivated by practical applications, the input may not be completely known in advance, but revealedduringtime. Inthiscase,knownastheon-linecase,thegoalistodesign algorithms that are able to produce solutions that are close to the best possible solution that can be produced by any o?-line algorithm, i. e. , an algorithm that knows the input in advance. 1 Theseissueshavebeentreatedinsomerecenttexts ,butinthelastfewyears a huge amount of new results have been produced in the area of approximation and on-line algorithms.
Complex analysis --- Discrete mathematics --- Computer science --- Computer architecture. Operating systems --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- discrete wiskunde --- complexe analyse (wiskunde) --- grafische vormgeving --- informatica --- algoritmen --- KI (kunstmatige intelligentie) --- computernetwerken --- numerieke analyse
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