Efficient Algorithms for Data Processing
Explore I/O efficient algorithms such as merge-sort, M/B-way merge, funnel sort, and more. Discover insights on buffer sizes and mergers' performance through Lemmas 1 and 2.
Uploaded on | 0 Views
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
Merge-sort M/B M/B M/B
M/B-way merge <M/B sorted lists of total size n can be merged in O(n/B) I/Os
Funnel sort N1/3 N2/9 N4/27
B 3 k M k
B 3 k M 1/2 k B B 3/2 3/2 k k M M 1/2 1/2 k k
B 3 k M 1/2 k B B 3/2 3/2 k k M 1/4 M k 1/2 k B B 3/4 3/4 k k M M 1/4 1/4 k k
Lemma 1: The size of a k-merger (excluding its input and output buffers) is O(k^2)
Lemma 2: The number of I/Os performed by a k-merger is 3 k B + logM O k k
Bibliography Paper that started the research: http://dl.acm.org/citation.cfm?id=48535 The cache oblivious model: http://dl.acm.org/citation.cfm?id=2071383 Larse Arge home page: http://www.madalgo.au.dk/~large/
