# Algebraic Rewritings for Optimizing Regular Path Queries

## Abstract

Rewriting queries using views is a powerful technique that has applications in query optimization, data integration, data warehousing etc. Query rewriting in relational databases is by now rather well investigated. However, in the framework of semistructured data the problem of rewriting has received much less attention. In this paper we focus on extracting as much information as possible from algebraic rewritings for the purpose of optimizing regular path queries. The cases when we can find a complete exact rewriting of a query using a set a views are very “ideal.” However, there is always information available in the views, even if this information is only partial. We introduce “lower” and “possibility” partial rewritings and provide algorithms for computing them. These rewritings are algebraic in their nature, i.e. we use only the algebraic view definitions for computing the rewritings. This fact makes them a main memory product which can be used for reducing secondary memory and remote access. We give two algorithms for utilizing the partial lower and partial possibility rewritings in the context of query optimization.

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### References

- [Abi97]S. Abiteboul. Querying Semistructured Data.
*Proc. of ICDT*1997 pp. 1–18.Google Scholar - [ABS99]S. Abiteboul, P. Buneman and D. Suciu.
*Data on the Web: From Relations to Semistructured Data and Xml*. Morgan Kaufmann, 1999.Google Scholar - [AD98]S. Abiteboul, O. M. Duschka. Complexity of Answering Queries Using Materialized Views.
*Proc. of PODS*1998 pp. 254–263Google Scholar - [AHV95]S. Abiteboul, R. Hull and V. Vianu.
*Foundations of Databases*. Addison-Wesley, 1995.Google Scholar - [AQM+97]S. Abiteboul, D. Quass, J. McHugh, J. Widom and J. L. Wiener. The Lorel Query Language for Semistructured Data.
*Int. J. on Digital Li-braries*1997 1(1) pp. 68–88.Google Scholar - [Bun97]P. Buneman. Semistructured Data.
*Proc. of PODS*1997, pp. 117–121.Google Scholar - [BDFS97]P. Buneman, S. B. Davidson, M. F. Fernandez and D. Suciu. Adding Structure to Unstructured Data.
*Proc. of ICDT*1997, pp. 336–350.Google Scholar - [CGLV99]D. Calvanese, G. Giacomo, M. Lenzerini and M. Y. Vardi. Rewriting of Regular Expressions and Regular Path Queries.
*Proc. of PODS*1999, pp. 194–204.Google Scholar - [CGLV2000]D. Calvanese, G. Giacomo, M. Lenzerini and M. Y. Vardi. Answering Regular Path Queries Using Views.
*Proc. of ICDE*2000, pp. 389–398.Google Scholar - [CGLV2000]D. Calvanese, G. Giacomo, M. Lenzerini and M. Y. Vardi. View-Based Query Processing for Regular Path Queries with Inverse.
*Proc. of PODS*2000, pp. 58–66.Google Scholar - [Con71]J. H. Conway.
*Regular Algebra and Finite Machines*. Chapman and Hall 1971.Google Scholar - [DFF+99]A. Deutsch, M. F. Fernandez, D. Florescu, A. Y. Levy, D. Suciu. A Query Language for XML.
*WWW8/Computer Networks 31(11-16)*1999, pp. 1155–116.Google Scholar - [DG97]O. Duschka and M. R. Genesereth. Answering Recursive Queries Using Views.
*Proc. of PODS*1997, pp. 109–116.Google Scholar - [FS98]M. F. Fernadez and D. Suciu. Optimizing Regular path Expressions Using Graph Schemas
*Proc. of ICDE*1998, pp. 14–23.Google Scholar - [FLS98]D. Florescu, A. Y. Levy, D. Suciu Query Containment for Conjunctive Queries with Regular Expressions
*Proc. of PODS*1998, pp. 139–148.Google Scholar - [GM99]G. Grahne and A. O. Mendelzon. Tableau Techniques for Querying Information Sources through Global Schemas.
*Proc. of ICDT*1999 pp. 332–347.Google Scholar - [GT2000]G. Grahne and A. Thomo. An Optimization Technique for Answering Regular Path Queries.
*Proc. of WebDB*2000.Google Scholar - [HU79]J. E. Hopcroft and J. D. Ullman
*Introduction to Automata Theory, Languages, and Computation*. Addison-Wesley 1979.Google Scholar - [HRS76]H. B. Hunt and D. J. Rosenkrantz, and T. G. Szymanski, On the Equivalence, Containment, and Covering Problems for the Regular and Context-Free Languages.
*Journal of Computing and System Sciences*12(2) 1976, pp. 222–268MATHMathSciNetGoogle Scholar - [Kari91]L. Kari.
*On Insertion and Deletion in Formal Languages*. Ph.D. Thesis, 1991, Department of Mathematics, University of Turku, Finland.Google Scholar - [Lev99]A. Y. Levy.
*Answering queries using views: a survey*. Submitted for publication 1999.Google Scholar - [LMSS95]A. Y. Levy, A. O. Mendelzon, Y. Sagiv, D. Srivastava. Answering Que-ries Using Views.
*Proc. of PODS*1995, pp. 95–104.Google Scholar - [MW95]A. O. Mendelzon and P. T. Wood, Finding Regular Simple Paths in Graph Databases.
*SIAM J. Comp. 24:6*, (December 1995).Google Scholar - [MMM97]A. O. Mendelzon, G. A. Mihaila and T. Milo. Querying theWorld Wide Web.
*Int. J. on Digital Libraries*1(1), 1997 pp. 54–67.Google Scholar - [MS99]T. Milo and D. Suciu. Index Structures for Path Expressions.
*Proc. of ICDT*, 1999, pp. 277–295.Google Scholar - [PV99]Y. Papakonstantinou, V. Vassalos. Query Rewriting for Semistructured Data.
*proc. of SIGMOD*1999, pp. 455–466Google Scholar - [Ull97]J. D. Ullman. Information Integration Using Logical Views.
*Proc. of ICDT*1997, pp. 19–40.Google Scholar - [Var88]M. Y. Vardi. The universal-relation model for logical independence.
*IEEE Software*.Google Scholar - [Yu97]S. Yu. Reqular Languages. In:
*Handbook of Formal Languages*. G. Ro-zenberg and A. Salomaa (Eds.). Springer Verlag 1997, pp. 41–110Google Scholar