Hybrid Transitive Closure Algorithms

We present a new family of hybrid transitive closure algorithms, and present experimental results showing that these algorithms perform better than existing transitive closure algorithms, includmg matrix-based algorithms that divide a matrix into stripes or into square blocks, and graph-based algmtihms. This family of algorithms can be generalized to solve path problems and to solve problems in which some selection criteria have been specified for source or destination nodes.

[1]  Patrick Valduriez,et al.  Evaluation of Recursive Queries Using Join Indices , 1986, Expert Database Conf..

[2]  T H Merrett,et al.  Relational Information Systems , 1983 .

[3]  Werner Kießling,et al.  On the Evaluation of Recursion in (Deductive) Database Systems by Efficient Differential Fixpoint Iteration , 1987, ICDE.

[4]  Stephen Warshall,et al.  A Theorem on Boolean Matrices , 1962, JACM.

[5]  Rakesh Agrawal.  Alpha: An extension of relational algebra to express a class of recursive queries , 1987, 1987 IEEE Third International Conference on Data Engineering.

[6]  Henry S. Warren,et al.  A modification of Warshall's algorithm for the transitive closure of binary relations , 1975, Commun. ACM.

[7]  Seppo Sippu,et al.  A generalized transitive closure for relational queries , 1988, PODS '88.

[8]  Yannis E. Ioannidis,et al.  On the Computation of the Transitive Closure of Relational Operators , 1986, VLDB.

[9]  Michael Stonebraker,et al.  Heuristic Search in Data Base Systems , 1984, Expert Database Workshop.

[10]  H. V. Jagadish,et al.  Direct transitive closure algorithms: design and performance evaluation , 1990, TODS.

[11]  Jürgen Ebert,et al.  A Sensitive Transitive Closure Algorithm , 1981, Inf. Process. Lett..

[12]  Paul Walton Purdom,et al.  A transitive closure algorithm , 1970, BIT.

[13]  Bin Jiang.  A suitable algorithm for computing partial transitive closures in databases , 1990, [1990] Proceedings. Sixth International Conference on Data Engineering.

[14]  Michael Stonebraker,et al.  Heuristic search in database systems , 1986 .

[15]  Raghu Ramakrishnan,et al.  Efficient Transitive Closure Algorithms , 1988, VLDB.

[16]  Hongjun Lu,et al.  New Strategies for Computing the Transitive Closure of a Database Relation , 1987, VLDB.

[17]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[18]  H. V. Jagadish,et al.  A study of transitive closure as a recursion mechanism , 1987, SIGMOD '87.

[19]  Bin Jiang,et al.  Making the Partial Transitive Closure an Elementary Database Operation , 1989, BTW.

[20]  DayalUmeshwar,et al.  Traversal recursion: a practical approach to supporting recursive applications , 1986 .

[21]  H. V. Jagadish,et al.  Direct Algorithms for Computing the Transitive Closure of Database Relations , 1987, VLDB.

[22]  François Bancilhon,et al.  Naive Evaluation of Recursively Defined Relations , 1986, On Knowledge Base Management Systems.

[23]  Umeshwar Dayal,et al.  Traversal recursion: a practical approach to supporting recursive applications , 1986, SIGMOD '86.

[24]  Theodore S. Norvell,et al.  Aggregative closure: an extension of transitive closure , 1989, [1989] Proceedings. Fifth International Conference on Data Engineering.