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Amortized Complexity of Data Structures, Vol. 255 (Classic Reprint)

Rajamani Sundar

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Description:Excerpt from Amortized Complexity of Data Structures, Vol. 255 This thesis investigates the amortized complexity of some fundamental data structure problems and introduces interesting ideas for proving lower bounds on amortized complexity and for performing amortized analysis. The problems are as follows: Dictionary Problem: A dictionary is a dynamic set that supports searches of elements and changes under insertions and deletions of elements. It is open whether there exists a dictionary data structure that takes constant amortized time per operation and uses space polynomial in the dictionary size. We prove that dictionary operations require log-logarithmic amortized time under a multilevel hashing model that is based on Yao's cell probe model. Splay Algorithm's Analysis: Splay is a simple, efficient algorithm for searching binary search trees, devised by Sleator and Tarjan, that uses rotations to reorganize the tree. Tarjan conjectured that Splay takes linear time to process deque operation sequences on a binary tree and proved a special case of this conjecture called the Scanning Theorem. We prove tight bounds on the maximum numbers of various types of right rotations in a sequence of right rotations performed on a binary tree. One of the lower bounds refutes a conjecture of Sleator. We apply the upper bounds to obtain a nearly linear upper bound for Tarjan's conjecture. We give two new proofs of the Scanning Theorem, one of which is a potential-based proof that solves a problem of Tarjan. Set Equality Problem: The task of maintaining a dynamic collection of sets under various operations arises in many applications. We devise a fast data structure for maintaining sets under equality-tests and under creations of new sets through insertions and deletions of elements. Equality-tests require constant time and set-creations require logarithmic amortized time. This improves previous solutions. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Amortized Complexity of Data Structures, Vol. 255 (Classic Reprint). To get started finding Amortized Complexity of Data Structures, Vol. 255 (Classic Reprint), you are right to find our website which has a comprehensive collection of manuals listed.
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Description: Excerpt from Amortized Complexity of Data Structures, Vol. 255 This thesis investigates the amortized complexity of some fundamental data structure problems and introduces interesting ideas for proving lower bounds on amortized complexity and for performing amortized analysis. The problems are as follows: Dictionary Problem: A dictionary is a dynamic set that supports searches of elements and changes under insertions and deletions of elements. It is open whether there exists a dictionary data structure that takes constant amortized time per operation and uses space polynomial in the dictionary size. We prove that dictionary operations require log-logarithmic amortized time under a multilevel hashing model that is based on Yao's cell probe model. Splay Algorithm's Analysis: Splay is a simple, efficient algorithm for searching binary search trees, devised by Sleator and Tarjan, that uses rotations to reorganize the tree. Tarjan conjectured that Splay takes linear time to process deque operation sequences on a binary tree and proved a special case of this conjecture called the Scanning Theorem. We prove tight bounds on the maximum numbers of various types of right rotations in a sequence of right rotations performed on a binary tree. One of the lower bounds refutes a conjecture of Sleator. We apply the upper bounds to obtain a nearly linear upper bound for Tarjan's conjecture. We give two new proofs of the Scanning Theorem, one of which is a potential-based proof that solves a problem of Tarjan. Set Equality Problem: The task of maintaining a dynamic collection of sets under various operations arises in many applications. We devise a fast data structure for maintaining sets under equality-tests and under creations of new sets through insertions and deletions of elements. Equality-tests require constant time and set-creations require logarithmic amortized time. This improves previous solutions. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Amortized Complexity of Data Structures, Vol. 255 (Classic Reprint). To get started finding Amortized Complexity of Data Structures, Vol. 255 (Classic Reprint), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Amortized Complexity of Data Structures, Vol. 255 (Classic Reprint)

Amortized Complexity of Data Structures, Vol. 255 (Classic Reprint)

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