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商品コード: 9781680836370

Semialgebraic Proofs and Efficient Algorithm

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書名

Semialgebraic Proofs and Efficient Algorithm Design
シリーズ名 Foundations and Trends in Theoretical Computer Science (Vol. 14, Issue 1-2)
著者・編者 Fleming, N. et al.
出版社/発行元 Now publishers
発行年/月 2019年12月   
装丁 電子ブック
ページ数/巻数

234 ページ

ISBN 978-1-68083-637-0

 


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Description

 

In the last two decades a link has been established that, in some cases, proof that a solution exists has enabled an algorithm to find that solution itself. This has had most effect on semialgebraic proof systems and linear and semidefinite programming.

This monograph details the interplay between proof systems and efficient algorithm design and surveys the state-of-the-art for two of the most important semi-algebraic proof systems: Sherali-Adams and Sum-of-Squares. It provides the readers with a rigorous treatment of these systems both as proof systems, and as a general family of optimization algorithms. The emphasis is on illustrating the main ideas by presenting a small fraction of representative results with detailed intuition and commentary. The monograph is self-contained and includes a review of the necessary mathematical background including basic theory of linear and semidefinite programming.

Semialgebraic Proofs and Efficient Algorithm Design provides the advanced reader with a deep insight into the exciting line of research. It will inspire readers in deploying the techniques in their own further research.

 

Contents:

 

1. Introduction
2. Sherali-Adams
3. Sum-of-Squares
4. Upper Bounds via Sum-of-Squares
5. Lower Bounds for Sum-of-Squares
Appendices
Acknowledgments
References
Index

 

 

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