Efficient algorithms for minimizing tree pattern queries

We consider the problem of minimizing tree pattern queries (TPQ) that arise in XML and in LDAP-style network directories. In [Minimization of Tree Pattern Queries, <i>Proc. ACM SIGMOD Intl. Conf. Management of Data,</i> 2001, pp. 497-508], Amer-Yahia, Cho, Lakshmanan and Srivastava presented an <i>O</i>(<i>n</i><sup>4</sup>) algorithm for minimizing TPQs in the absence of integrity constraints (Case 1); <i>n</i> is the number of nodes in the query. Then they considered the problem of minimizing TPQs in the presence of three kinds of integrity constraints: required-child, required-descendant and subtype (Case 2). They presented an <i>O</i>(<i>n</i><sup>6</sup>) algorithm for minimizing TPQs in the presence of only required-child and required-descendant constraints (i.e., no subtypes allowed; Case 3). We present <i>O</i>(<i>n</i><sup>2</sup>), <i>O</i>(<i>n</i><sup>4</sup>) and <i>O</i>(<i>n</i><sup>2</sup>) algorithms for minimizing TPQs in these three cases, respectively, based on the concept of graph simulation. We believe that our <i>O</i>(<i>n</i><sup>2</sup>) algorithms for Cases 1 and 3 are runtime optimal.

[1]  Ashok K. Chandra,et al.  Optimal implementation of conjunctive queries in relational data bases , 1977, STOC '77.

[2]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[3]  David Maier,et al.  Testing implications of data dependencies , 1979, SIGMOD '79.

[4]  Jeffrey D. Ullman,et al.  Principles of Database and Knowledge-Base Systems, Volume II , 1988, Principles of computer science series.

[5]  Jeffrey D. Uuman.  Principles of database and knowledge- base systems , 1989 .

[6]  Bard Bloom,et al.  Transformational Design and Implementation of a New Efficient Solution to the Ready Simulation Problem , 1995, Sci. Comput. Program..

[7]  J W Ballard,et al.  Data on the web? , 1995, Science.

[8]  Thomas A. Henzinger,et al.  Computing simulations on finite and infinite graphs , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[9]  Dan Suciu,et al.  Adding Structure to Unstructured Data , 1997, ICDT.

[10]  Diego Calvanese,et al.  Dwq : Esprit Long Term Research Project, No 22469 on the Decidability of Query Containment under Constraints on the Decidability of Query Containment under Constraints , 2022 .

[11]  Dan Suciu,et al.  Query containment for conjunctive queries with regular expressions , 1998, PODS.

[12]  Alin Deutsch,et al.  A Query Language for XML , 1999, Comput. Networks.

[13]  Laks V. S. Lakshmanan,et al.  Querying network directories , 1999, SIGMOD '99.

[14]  Peter T. Wood,et al.  Optimising Web queries using document type definitions , 1999, WIDM '99.

[15]  Daniela Florescu,et al.  Quilt: An XML Query Language for Heterogeneous Data Sources , 2000, WebDB.

[16]  Peter T. Wood,et al.  Rewriting XQL Queries on XML Repositories , 2000, BNCOD.

[17]  Wenfei Fan,et al.  Integrity constraints for XML , 2000, PODS.

[18]  Peter T. Wood,et al.  On the Equivalence of XML Patterns , 2000, Computational Logic.

[19]  Yannis Papakonstantinou,et al.  DTD inference for views of XML data , 2000, PODS.

[20]  Peter T. Wood.  Minimising Simple XPath Expressions , 2001, WebDB.

[21]  Laks V. S. Lakshmanan,et al.  Minimization of tree pattern queries , 2001, SIGMOD '01.

[22]  Dan Suciu,et al.  Containment and equivalence for an XPath fragment , 2002, PODS.

[23]  T. Howes,et al.  Understanding and Deploying LDAP Directory Services , 2003 .