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In the standard setting of online computation, the input is not entirely available from the beginning, but is revealed incrementally, piece by piece, as a sequence of requests. Whenever a request arrives, the online algorithm has to make immediately irrevocable decisions to serve the request, without knowledge on the future requests. Usually, the standard framework to evaluate the performance of online algorithms is competitive analysis, which compares the worst-case performance of an online algorithm to an offline optimal solution. In this thesis, we will study some new ways of looking at online problems. First, we study the online computation in the recourse model, in which the irrevocability on online decisions is relaxed. In other words, the online algorithm is allowed to go back and change previously made decisions. More precisely, we show how to identify the trade-off between the number of re-optimization and the performance of online algorithms for the online maximum matching problem. Moreover, we study measures other than competitive analysis for evaluating the performance of online algorithms. We observe that sometimes, competitive analysis cannot distinguish the performance of different algorithms due to the worst-case nature of the competitive ratio. We demonstrate that a similar situation arises in the linear search problem. More precisely, we revisit the linear search problem and introduce a measure, which can be applied as a refinement of the competitive ratio. Last, we study the online computation in the advice model, in which the algorithm receives as input not only a sequence of requests, but also some advice on the request sequence. Specifically, we study a recent model with untrusted advice, in which the advice can be either trusted or untrusted. Assume that in the latter case, the advice can be generated from a malicious source. We show how to identify a Pareto optimal strategy for the online bidding problem in the untrusted advice model.
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.
The interaction paradigm is a new conceptualization of computational phenomena that emphasizes interaction over algorithms, reflecting the shift in technology from main-frame number-crunching to distributed intelligent networks with graphical user interfaces. The book is arranged in four sections: "Introduction", comprising three chapters that explore and summarize the fundamentals of interactive computation; "Theory" with six chapters, each discussing a specific aspect of interaction; "Applications," five chapters showing how this principle is applied in subdisciplines of computer science; and "New Directions," presenting four multidisciplinary applications. The book challenges traditional Turing machine-based answers to fundamental questions of problem solving and the scope of computation.
The refereed proceedings of the 14th Annual International Computing and Combinatorics Conference, COCOON 2008, held in Dalian, China, in June 2008. The 66 revised full papers presented were carefully reviewed and selected from 172 submissions. The papers are organized in topical sections on algorithms and data structures, algorithmic game theory and online algorithms, automata, languages, logic, and computability, combinatorics related to algorithms and complexity, complexity theory, cryptography, reliability and security, and database theory, computational biology and bioinformatics, computational algebra, geometry, and number theory, graph drawing and information visualization, graph theory and algorithms, communication networks, and optimization, wireless network, network optimization, and scheduling problem.
This book constitutes the refereed proceedings of the 19th International Conference on Computing and Combinatorics, COCOON 2013, held in Hangzhou, China, in June 2013. The 56 revised full papers presented were carefully reviewed and selected from 120 submissions. There was a co-organized workshop on discrete algorithms of which 8 short papers were accepted and a workshop on computational social networks where 12 papers out of 25 submissions were accepted.
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
Thepapersinthisvolumewereselectedforpresentationatthe10thInternational Computing and Combinatorics Conference (COCOON 2004), held on August 17–20, 2004 in Jeju Island, Korea. Previous meetings were held in Xi’an (1995), HongKong(1996),Shanghai(1997),Taipei(1998),Tokyo(1999),Sydney(2000), Guilin (2001), Singapore (2002), and Big Sky (2003). In response to the call for papers, 109 extended abstracts were submitted from 23 countries, of which 46 were accepted. The submitted papers were from Belgium (1), Canada (5), China (6), France (1), Germany (6), Hong Kong (8), India (6), Iran (1), Ireland (1), Israel (4), Italy (2), Japan (17), Korea (23), Mexico (3), New Zealand (1), Poland(1), Russia (1), Singapore (5), Sweden (2), Switzerland (3), Taiwan (2), the UK (1), and the USA (9). Each paper was evaluated by at least three program committee members, with the assistance of referees, as indicated by the referee list found in these proceedings. There were many more acceptable papers than there was space available in the conference schedule, and the program committee’s task was extremely di?cult. In addition to selected papers, the conference also included threeinvitedpresentationsbyLarsArge,JeongHanKim,andKokichiSugihara. We thank all program committee members and their referees for their - cellent work, especially given the demanding time constraints; they gave the conference its distinctive character. We thank all who submitted papers for c- sideration: they all contributed to the high quality of the conference. Finally,wethankallthepeoplewhoworkedhardtoputinplacethelogistical arrangements of the conference — our colleagues and our graduate students. It is their hard work that made the conference possible and enjoyable.