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Abstract: It is well-known that the computation cost to find the transitive closure (TC) of a graph stored as an adjacency matrix is the same, to within a constant factor, as matrix multiplication. In this paper, we present a new TC algorithm based on double hashing and two-dimensionally organized files. We show that, when using this algorithm, the computation and i/o costs of finding the TC of a database relation is like that of performing a relational composition operation. For sparse closures, sparse... (Update)
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BibTeX entry: (Update)
@inproceedings{ taylor91direct,
author = "Steve Taylor and Nabil I. Hachem",
title = "A Direct Algorithm for Computing the Transitive Closure of a Two-Dimensionally Structured File",
booktitle = "Mathematical Fundamentals of Database Systems",
pages = "146-159",
year = "1991",
url = "citeseer.ist.psu.edu/taylor91direct.html" }
Citations (may not include all citations):1450 The Design and Analysis of Computer Algorithms (context) - Aho, Hopcroft et al. - 1974
308 Matrix Multiplication via Arithmetic Progressions (context) - Coppersmith, Winograd - 1987
192 Representation of Events in Nerve Nets and Finite Automata (context) - Kleene - 1956
86 A Theorem on Boolean Matrices (context) - Warshall - 1962
32 Alpha: An extension of Relational Algebra to Express a Class.. (context) - Agrawal
27 Efficient Transitive Closure Algorithms (context) - Ioannidis, Ramakrishnan
22 the Computation of the Transitive Closure of Relational Oper.. (context) - Ioannidis
19 Evaluation of Recursive Queries Using Join Indices (context) - Valduriez, Boral - 1986
17 A Study of Transitive Closure as a Recursion mechanism (context) - Jagadish, Agrawal et al. - 1987
15 Direct Algorithms for Computing the Transitive Closure of Da.. (context) - Agrawal, Jagadish
14 Hybrid Transitive Closure Algorithms - Agrawal, Jagadish
13 New Strategies for Computing the Transitive Closure of a Dat.. (context) - Lu
11 A Modification of Warshall's Algorithm for the Transitive Cl.. (context) - Warren - 1975
10 What You Always Wanted to Know About Datalog (And Never Dare.. (context) - Ceri, Gottlob et al. - 1989
3 The Input/Output Complexity of Transitive Closure (context) - Ullman, Yannakakis
3 The Processing and Evaluation of Transitive Closure Queries (context) - Han, Qadeh et al.
2 An Amateur Introduction to Recursive Query Processing (context) - Bancilhon, Ramakrishna - 1986
1 Database and Knowledge-base Systems Vol II (context) - Ullman - 1989
1 A Parallel Transitive Closure Algorithm using hashs-based cl.. (context) - Cheiney, de Maindreville - 1989
1 Composition of Database Relations (context) - Agrawal, Dar et al.
1 Implementation of an Efficient Transitive Closure Operation .. (context) - Hachem - 1990
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