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In-Depth Information
ies that are also expressed as GLAV mappings coincide with relaxed chase-inverses
(Note that extended inverses and maximum extended recoveries, or any of the
other semantic notions of inverses, need not be expressible as GLAV mappings,
in general). This correspondence between two very general semantic notions, on
the one hand, and two procedural and practical notions of inverses, on the other, is
interesting in itself.
Finally, we note that there are certain limitations to what composition and inver-
sion can achieve in the context of schema evolution. For example, if we refer back
to Fig.
7.1
, it is conceivable that the composition
M
ı
M
0
does not always give the
“complete” mapping from
S
to
T
0
. Instead, the “complete” mapping from
S
to
T
0
may require
merging
the schema mapping
M
ı
M
0
with an additional mapping that
relates directly
S
to
T
0
. Such additional mapping may be defined separately by a user
to account for, say, a schema element that occurs in both
S
and
T
0
but does not occur
in
T
. The operation of merging two schema mappings appears in the model man-
agement framework [
Melnik et al. 2005
] under the term
Confluence
; a more refined
version of merge, together with an algorithm for it, appears in
Alexe et al.
[
2010
].
8
Concluding Remarks
In this chapter, we illustrated how the composition operator and the inverse operator
on schema mappings can be applied to schema evolution. The techniques presented
here rely on the existence of chase-inverses or relaxed chase-inverses, which, in
particular, are required to be specified by GLAV constraints. Much more remains
to be done in the study of schema mappings for which no relaxed chase-inverse
exists. In this direction, research issues include: (1) What is the exact language for
expressing maximum extended recoveries? (2) How does this language compose
with SO tgds? (3) What do inverses of SO tgds look like? More broadly, is there a
unifying schema-mapping language that is closed under both composition and the
various flavors of inverses, and, additionally, has good algorithmic properties?
Acknowledgements
The authors thank Erhard Rahm for reading an earlier version of this chapter
and providing valuable feedback. The research of Kolaitis and Tan is supported by NSF grant IIS-
0430994 and NSF grant IIS-0905276. Tan is also supported by NSF CAREER award IIS-0347065.
References
Alexe B, Hernandez MA, Popa L, Tan WC (2010) MapMerge: Correlating independent schema
mappings. In: PVLDB, vol 3(1), pp 81-92
Arenas M, Perez J, Riveros C (2008) The recovery of a schema mapping: Bringing exchanged data
back. In: PODS. ACM, NY, pp 13-22
Bernstein PA (2003) Applying model management to classical meta-data problems. In: Conference
on innovative data systems research (CIDR), Asilomar, CA, pp 209-220
Bernstein PA, Green TJ, Melnik S, Nash A (2008) Implementing mapping composition. VLDB J
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