Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Expert Solution & Answer
Chapter 16, Problem 12PE
Explanation of Solution
Proof:
- Let the number of join orders will be,
- A complete binary tree consists of several internal nodes and each internal node contains exactly 2 children.
- Each join order is considered as a complete binary tree and in which all the relations are considered as the leaves.
- There is a bijection between the count of binary tress of “n-1” nodes and count of binary trees of “n” leaves when considering a
database with “n” relations (leaf nodes). - Hence, the total number of created binary trees are,
- Each complete binary tree of “n” leaves will contain “n-1” nodes.
- Conversely, add “n” leaves to the binary tree to make this tree to a complete binary tree.
- The number of binary trees that contains “n-1” nodes is,
Expert Solution & Answer
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Check out a sample textbook solutionChapter 16 Solutions
Database System Concepts
Ch. 16 - Prob. 2PECh. 16 - Prob. 3PECh. 16 - SQL allows relations with duplicates (Chapter 3),...Ch. 16 - Prob. 5PECh. 16 - Prob. 6PECh. 16 - Prob. 7PECh. 16 - Prob. 8PECh. 16 - Prob. 9PECh. 16 - Prob. 10PECh. 16 - Prob. 12PE
Ch. 16 - Prob. 13PECh. 16 - Prob. 14PECh. 16 - Prob. 16ECh. 16 - Prob. 17ECh. 16 - Prob. 19ECh. 16 - Explain how to use a histogram to estimate the...Ch. 16 - Prob. 21ECh. 16 - Prob. 22ECh. 16 - Describe how to incrementally maintain the results...Ch. 16 - Prob. 24ECh. 16 - Prob. 25ECh. 16 - Prob. 26ECh. 16 - Prob. 27E
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