A Simple Greedy Algorithm for Finding Functional Relations: Efficient Implementation and Average Case Analysis
 Tatsuya Akutsu,
 Satoru Miyano,
 Satoru Kuhara
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Abstract
Inferring functional relations from relational databases is important for discovery of scientific knowledge because many experimental data in science are represented in the form of tables and many rules are represented in the form of functions. A simple greedy algorithm has been known as an approximation algorithm for this problem. In this algorithm, the original problem is reduced to the set cover problem and a wellknown greedy algorithm for the set cover is applied. This paper shows an efficient implementation of this algorithm that is specialized for inference of functional relations. If one functional relation for one output variable is required, each iteration step of the greedy algorithm can be executed in linear time. If functional relations for multiple output variables are required, it uses fast matrix multiplication in order to obtain nontrivial time complexity bound. In the former case, the algorithm is very simple and thus practical. This paper also shows that the algorithm can find an exact solution for simple functions if input data for each function are generated uniformly at random and the size of the domain is bounded by a constant. Results of preliminary computational experiments on the algorithm are described too.
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 Title
 A Simple Greedy Algorithm for Finding Functional Relations: Efficient Implementation and Average Case Analysis
 Book Title
 Discovery Science
 Book Subtitle
 Third International Conference, DS 2000 Kyoto, Japan, December 4–6, 2000 Proceedings
 Pages
 pp 8698
 Copyright
 2000
 DOI
 10.1007/3540444181_8
 Print ISBN
 9783540413523
 Online ISBN
 9783540444183
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1967
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
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 Editors

 Setsuo Arikawa ^{(1)}
 Shinichi Morishita ^{(2)}
 Editor Affiliations

 1. Faculty of Information Science and Electrical Engineering, Department of Informatics, Kyushu University
 2. Faculty of Science Department of Information Science, University of Tokyo
 Authors

 Tatsuya Akutsu ^{(5)}
 Satoru Miyano ^{(5)}
 Satoru Kuhara ^{(6)}
 Author Affiliations

 5. Human Genome Center, Institute of Medical Science, University of Tokyo, 461 Shirokanedai, 1088639, Tokyo, Minatnoku, Japan
 6. Graduate School of Genetic Resources Technology, Kyushu University, Hakozaki, 8128581, Higashiku, Fukuoka, Japan
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