Data structures and network algorithms
Data structures and network algorithms
ACM Computing Surveys (CSUR)
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IEEE Transactions on Software Engineering - Annals of discrete mathematics, 24
Query optimization by semantic reasoning
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SIGMOD '86 Proceedings of the 1986 ACM SIGMOD international conference on Management of data
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STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
ACM Transactions on Database Systems (TODS)
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Journal of the ACM (JACM)
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SIGMOD '89 Proceedings of the 1989 ACM SIGMOD international conference on Management of data
Logic-based approach to semantic query optimization
ACM Transactions on Database Systems (TODS)
Data structures and algorithm analysis
Data structures and algorithm analysis
Query Optimization in Database Systems
ACM Computing Surveys (CSUR)
Data Structures and Algorithms
Data Structures and Algorithms
SIGMOD '83 Proceedings of the 1983 ACM SIGMOD international conference on Management of data
Horizontal data partitioning in database design
SIGMOD '82 Proceedings of the 1982 ACM SIGMOD international conference on Management of data
Common expression analysis in database applications
SIGMOD '82 Proceedings of the 1982 ACM SIGMOD international conference on Management of data
Design and Implementation of a Semantic Query Optimizer
IEEE Transactions on Knowledge and Data Engineering
Automatic Knowledge Acquisition and Maintenance for Semantic Query Optimization
IEEE Transactions on Knowledge and Data Engineering
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IEEE Transactions on Knowledge and Data Engineering
Semantic Query Optimization for Tree and Chain Queries
IEEE Transactions on Knowledge and Data Engineering
Updating Derived Relations: Detecting Irrelevant and Autonomously Computable Updates
VLDB '86 Proceedings of the 12th International Conference on Very Large Data Bases
Solving satisfiability and implication problems in database systems
ACM Transactions on Database Systems (TODS)
IEEE Transactions on Knowledge and Data Engineering
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Implication testing of arithmetic inequalities has been widely used in different areas in database systems and has received extensive research as well. Klug and Ullman (A. Klug, 1988; and J.D. Ullman, 1989) proposed an algorithm that determines whether S implies T, where T and S consist of inequalities of form (X op Y), X and Y are two variables, and op驴{=, , 驴}. The complexity of the algorithm is O(n鲁), where n is the number of inequalities in S. We reduce the problem to matrix multiplication, thus improving the time bound to O(n^2.376). We also demonstrate an O(n虏) algorithm if the number of inequalities in T is bounded by O(n). Since matrix multiplication has been well studied, our reduction allows the possibility of directly adopting many practical results for managing matrices and their operations, such as parallel computation and efficient representation of sparse matrices.