Synopsis
Excerpt from Balancing Is Not Always Good
Note that if A2f>0 (f is strictly convex) then all the inequalities in the last proof are tight, and the decomposition that achieves the minimum in is unique.
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About the Author
Snir is Senior Manager, Scalable Parallel Systems, IBM Research Division.
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Balancing Is Not Always Good (Classic Reprint)
Print on DemandSeller: Forgotten Books, London, United Kingdom
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Paperback. Condition: New. Print on Demand. This book delves into the complexities of recurrence relations that arise within divide and conquer algorithms, challenging the commonly held notion known as the "Balancing Principle." The author meticulously examines scenarios where the principle stands valid, discerning that it holds true when the function representing the cost of combining solutions, denoted as f, exhibits convexity. However, when f demonstrates concavity, an optimal solution is achieved by deliberately introducing imbalance. The author meticulously formulates recurrence relations to express the time complexity of divide and conquer algorithms, establishing a functional equation framework for analysis. Through the study of convex and concave functions, the book illuminates the conditions under which the Balancing Principle remains valid. Expanding on this, the author presents a strategy for solving recurrence relations involving concave functions, thereby revealing that the optimal strategy in such cases involves unbalancing rather than maintaining equal-sized subproblems. This book significantly contributes to the theoretical understanding of algorithm analysis, particularly in the context of divide and conquer approaches. Its insights challenge conventional wisdom and provide valuable guidance for researchers and practitioners seeking to optimize the performance of algorithms. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781332869916_0
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Balancing Is Not Always Good Classic Reprint
Seller: PBShop.store US, Wood Dale, IL, U.S.A.
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332869916
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Balancing Is Not Always Good Classic Reprint
Seller: PBShop.store UK, Fairford, GLOS, United Kingdom
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332869916
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Balancing Is Not Always Good (Classic Reprint)
Seller: Revaluation Books, Exeter, United Kingdom
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Paperback. Condition: Brand New. 30 pages. 9.21x5.98x0.10 inches. In Stock. Seller Inventory # __1332869912
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Balancing Is Not Always Good (Classic Reprint)
Print on DemandSeller: Revaluation Books, Exeter, United Kingdom
Seller rating 5 out of 5 stars
Paperback. Condition: Brand New. 30 pages. 9.21x5.98x0.10 inches. In Stock. This item is printed on demand. Seller Inventory # 1332869912