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Tree-width and functional dependencies in databases

Published: 09 June 2008 Publication History

Abstract

Conjunctive query (CQ) evaluation on relational databases is NP-complete in general. Several restrictions, like bounded tree-width and bounded hypertree-width, allow polynomial time evaluations.We extend the framework in the presence of functional dependencies. Our exteAnded CQ evaluation problem has a concise equivalent formulation in terms of the homomorphism problem (HOM) for non-relational structures. We introduce the notions of "closure tree-width" and "hyperclosure tree-width" for arbitrary structures, and we prove that HOM (and hence CQ) restricted to bounded (hyper)closure tree-width becomes tractable. There are classes of structures with bounded closure tree-width but unbounded tree-width. Similar statements hold for hyperclosure tree-width and hypertree-width, and for hyperclosure tree-width and closure tree-width.
It follows from a result by Gottlob, Miklós, and Schwentick that for fixed k ≥ 2, deciding whether a given structure has hyperclosure tree-width at most k, is NP-complete. We prove an analogous statement for closure tree-width. Nevertheless, for given k we can approximate k-bounded closure tree-width in polynomial time.

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Cited By

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  • (2013)Structural tractability of enumerating CSP solutionsConstraints10.1007/s10601-012-9129-818:1(38-74)Online publication date: 1-Jan-2013
  • (2012)Tree-width for first order formulaeLogical Methods in Computer Science10.2168/LMCS-8(1:32)2012Volume 8, Issue 1Online publication date: 29-Mar-2012
  • (2010)Graphical models for dependencies and queries in uncertain data2010 IEEE 26th International Conference on Data Engineering Workshops (ICDEW 2010)10.1109/ICDEW.2010.5452725(301-304)Online publication date: Mar-2010

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cover image ACM Conferences
PODS '08: Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
June 2008
330 pages
ISBN:9781605581521
DOI:10.1145/1376916
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 09 June 2008

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Author Tags

  1. conjunctive queries
  2. databases
  3. functional dependencies
  4. hypertree-width
  5. tree-width

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PODS '08 Paper Acceptance Rate 28 of 159 submissions, 18%;
Overall Acceptance Rate 642 of 2,707 submissions, 24%

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Cited By

View all
  • (2013)Structural tractability of enumerating CSP solutionsConstraints10.1007/s10601-012-9129-818:1(38-74)Online publication date: 1-Jan-2013
  • (2012)Tree-width for first order formulaeLogical Methods in Computer Science10.2168/LMCS-8(1:32)2012Volume 8, Issue 1Online publication date: 29-Mar-2012
  • (2010)Graphical models for dependencies and queries in uncertain data2010 IEEE 26th International Conference on Data Engineering Workshops (ICDEW 2010)10.1109/ICDEW.2010.5452725(301-304)Online publication date: Mar-2010

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