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Titlebook: Exact Exponential Algorithms; Fedor V. Fomin,Dieter Kratsch Textbook 2010 Springer-Verlag Berlin Heidelberg 2010 Branching.Combinatorics.D

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发表于 2025-3-21 16:49:55 | 显示全部楼层 |阅读模式
书目名称Exact Exponential Algorithms
编辑Fedor V. Fomin,Dieter Kratsch
视频video
概述Textbook has been class-tested by the authors and their collaborators.Text is supported throughout with exercises and notes for further reading.Comprehensive introduction for researchers.Includes supp
丛书名称Texts in Theoretical Computer Science. An EATCS Series
图书封面Titlebook: Exact Exponential Algorithms;  Fedor V. Fomin,Dieter Kratsch Textbook 2010 Springer-Verlag Berlin Heidelberg 2010 Branching.Combinatorics.D
描述For a long time computer scientists have distinguished between fast and slow algo rithms. Fast (or good) algorithms are the algorithms that run in polynomial time, which means that the number of steps required for the algorithm to solve a problem is bounded by some polynomial in the length of the input. All other algorithms are slow (or bad). The running time of slow algorithms is usually exponential. This book is about bad algorithms. There are several reasons why we are interested in exponential time algorithms. Most of us believe that there are many natural problems which cannot be solved by polynomial time algorithms. The most famous and oldest family of hard problems is the family of NP complete problems. Most likely there are no polynomial time al gorithms solving these hard problems and in the worst case scenario the exponential running time is unavoidable. Every combinatorial problem is solvable in ?nite time by enumerating all possi ble solutions, i. e. by brute force search. But is brute force search always unavoid able? De?nitely not. Already in the nineteen sixties and seventies it was known that some NP complete problems can be solved signi?cantly faster than by brute
出版日期Textbook 2010
关键词Branching; Combinatorics; Dynamic programming; Exact algorithms; Exponential algorithms; Graph; Hard optim
版次1
doihttps://doi.org/10.1007/978-3-642-16533-7
isbn_softcover978-3-642-26566-2
isbn_ebook978-3-642-16533-7Series ISSN 1862-4499 Series E-ISSN 1862-4502
issn_series 1862-4499
copyrightSpringer-Verlag Berlin Heidelberg 2010
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发表于 2025-3-21 23:23:40 | 显示全部楼层
Branching,shed fast exponential time algorithms are branching algorithms. Furthermore, for many NP-hard problems the fastest known exact algorithm is a branching algorithm. Many of those algorithms have been developed during the last ten years by applying techniques like Measure & Conquer, quasiconvex analysi
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Dynamic Programming,ning polynomial time algorithms as well as for designing exponential time algorithms. The main idea of dynamic programming is to start by solving small or trivial instances and then gradually resolving larger and harder subproblems by composing solutions from smaller subproblems. From this point of
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Subset Convolution,algorithm one relies on repeated use of dynamic programming, and in particular on the so-called fast zeta transform. In the latter sections we present various algorithmic applications of fast subset convolution. In this chapter the algorithms (may) operate with large numbers and thus we use the log-
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Local Search and SAT,based on performing local search in balls in the Hamming space around some assignments. The first algorithm randomly chooses an assignment and performs a random walk of short length (in Hamming distance) to search for the solution. The second algorithm is deterministic and uses a similar idea; but i
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Split and List,ply these algorithms on hard problems, we (exponentially) enlarge the size of a hard problem and apply fast polynomial time algorithm on an input of exponential size. The common way to enlarge the problem is to split the input into parts, and for each part to enumerate (or list) all possible solutio
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