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Contains theoretical foundations, applications, and examples of competitive analysis for online algorithms.
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
There are no silver bullets in algorithm design, and no single algorithmic idea is powerful and flexible enough to solve every computational problem. Nor are there silver bullets in algorithm analysis, as the most enlightening method for analyzing an algorithm often depends on the problem and the application. However, typical algorithms courses rely almost entirely on a single analysis framework, that of worst-case analysis, wherein an algorithm is assessed by its worst performance on any input of a given size. The purpose of this book is to popularize several alternatives to worst-case analysis and their most notable algorithmic applications, from clustering to linear programming to neural network training. Forty leading researchers have contributed introductions to different facets of this field, emphasizing the most important models and results, many of which can be taught in lectures to beginning graduate students in theoretical computer science and machine learning.
This book constitutes the refereed proceedings of the 4th Italian Conference on Algorithms and Complexity, CIAC 2000, held in Rome, Italy, in March 2000. The 21 revised full papers presented were carefully reviewed and selected from 41 submissions; also included are four invited survey papers. Among the topics addressed are combinatorial optimization, graph algorithms, graph computations, complexity theory, diagram design, approximation, scheduling, sorting, computational geometry, searching, and pattern matching.
This book constitutes the thoroughly refereed post workshop proceedings of the 7th International Workshop on Approximation and Online Algorithms, WAOA 2009, held in Copenhagen, Denmark, in September 2009 as part of the ALGO 2009 conference event. The 22 revised full papers presented were carefully reviewed and selected from 62 submissions. The workshop covered areas such as algorithmic game theory, approximation classes, coloring and partitioning, competitive analysis, computational finance, cuts and connectivity, geometric problems, inapproximability results, mechanism design, network design, packing and covering, paradigms for design and analysis of approximation and online algorithms, parameterized complexity, randomization techniques, real-world applications, and scheduling problems.
This book constitutes the refereed proceedings of the 37th Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2011, held in Nový, Smokovec, Slovakia in January 2011. The 41 revised full papers, presented together with 5 invited contributions, were carefully reviewed and selected from 122 submissions. SOFSEM 2011 was organized around the following four tracks: foundations of computer science; software, systems, and services; processing large datasets; and cryptography, security, and trust.
This book constitutes the thoroughly refereed post-proceedings of the Second Symposium on Trustworthy Global Computing, TGC 2006, held in Lucca, Italy, in November 2006. The 14 revised papers presented together with two keynote lectures were carefully reviewed and selected from 32 submissions. The book starts off with activity reviews of four FP6 programmes of the European Union: Aeolus, Mobius, Sensoria, and Catnets.
This volume contains the invited and the contributed papers selected for p- th sentation at SOFSEM 2008, the 34 Conference on Current Trends in Theory and Practice of Computer Science, which was held January 19-25, 2008, in the Atrium Hotel, Novy þ Smokovec, High Tatras in Slovakia. SOFSEM (originally SOFtware SEMinar), as an annual international c- ference devoted to the theory and practice of computer science, aims to foster cooperationamongprofessionalsfromacademiaandindustryworkinginallareas in this?eld. Developing over the years from a local event to a fully international and well-established conference, contemporary SOFSEM continues to maintain the best of its original Winter School aspects, such as a high number of invited talks and in-depth coverage of novel research results in selected areas within computer science. SOFSEM 2008 was organized around the following tracks: - Foundations of Computer Science (Chair: Juhani Karhum· aki) - Computing by Nature (Chair: Alberto Bertoni) - Networks, Security, and Cryptography (Chair: Bart Preneel) - Web Technologies (Chair: Pavol Nþ avrat) The SOFSEM 2008 Program Committee consisted of 75 international - perts, representing active areas of the SOFSEM 2008 tracks with outstanding expertise and an eye for current developments, evaluating the submissions with the help of 169 additional reviewers. An integral part of SOFSEM 2008 was the traditional Student Research - rum (chaired by Ma þria Bielikovþ a), organized with the aim of presenting student projectsinthetheoryandpracticeofcomputerscienceandtogivestudentsfe- back on both originality of their scienti?c results and on their work in progress.
This book constitutes the refereed proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2010, held in Špindleruv Mlýn, Czech Republic, in January 2009. The 53 revised full papers, presented together with 11 invited contributions, were carefully reviewed and selected from 134 submissions. SOFSEM 2010 was organized around the following four tracks: Foundations of computer science, principles of software construction, Data, knowledge, and intelligent systems and Web science.
This textbook explains online computation in different settings, with particular emphasis on randomization and advice complexity. These settings are analyzed for various online problems such as the paging problem, the k-server problem, job shop scheduling, the knapsack problem, the bit guessing problem, and problems on graphs. This book is appropriate for undergraduate and graduate students of computer science, assuming a basic knowledge in algorithmics and discrete mathematics. Also researchers will find this a valuable reference for the recent field of advice complexity.