Using Semi-Joins to Solve Relational Queries
Journal of the ACM (JACM)
On the Desirability of Acyclic Database Schemes
Journal of the ACM (JACM)
Principles of Database Systems
Principles of Database Systems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
GYO reductions, canonical connections, tree and cyclic schemas and tree projections
PODS '83 Proceedings of the 2nd ACM SIGACT-SIGMOD symposium on Principles of database systems
The tree property is fundamental for query processing
PODS '82 Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systems
Transforming cyclic schemas into trees
PODS '82 Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systems
Properties of acyclic database schemes
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
The equivalence of solving queries and producing tree projections (extended abstract)
PODS '86 Proceedings of the fifth ACM SIGACT-SIGMOD symposium on Principles of database systems
Solving queries by tree projections
ACM Transactions on Database Systems (TODS)
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Relational database schemes can be partitioned into acyclic (tree) schemes and cyclic schemes. This partitioning also classifies the natural join queries into tree queries and cyclic queries. The problems of determining the minimum number of joins needed (i) to transform a cyclic scheme into an acyclic one, and (ii) to solve a cyclic query are shown [GS1 82, GS2 82] to be two different NP-complete problems. We consider a class of database schemes, called simple schemes. We show that the two problems above are equivalent but remain to be NP-complete when they are restricted to simple schemes. We give a polynomial time algorithm for both problems on simple schemes whose qual graphs are chordal. As a by-product, we also show that an edge contraction problem on undirected graphs is NP-complete and it is polynomial when the graph is chordal.