8 Using Qualitative Information in Query Proc. over Multiresolution Maps
169
8.3.3 Query Processing in GIS Mediation Architectures
The second scenario deals with mediation systems. The basic architecture of a mediation system is based on two main components: the mediator and the wrappers. We
focus our attention on the mediator that rewrites the user’s query into local queries,
afterwards translated by the wrapper in the data source query language (see Chap. 7).
In general, mediators do not consider, in query rewriting, the possible change of
spatial relations caused by multiresolution. As an example, assume that the maps in
Fig. 8.4 represent three local sources to be integrated and that, at the global level,
features are represented with the maximal dimension by which they appear in the
local sources. In our example, this means that at the global level, roads, towns, and
pollution areas are represented as regions. Actually, in more general cases, the choice
of feature dimensions depends on the user’s application and needs; moreover, it is
possible to create specific interfaces that may impose their own feature representation
to the users.
Suppose now that the user, at the global level, wants to know the roads that
enter town T 1 from North to NorthEast. As we will see in Sect. 8.5, this query can
be specified as follows:
Q 2 = {r|r is a road, r Overlap T 1 and r MBB:N:NE T 1 }.
As predicates Overlap and MBB:N:NE may not be defined over some local
sources, such query may not return any result from some of them. For each local
source, a more reasonable approach would be that of rewriting such predicates into
a set of predicates which are consistent with the given ones and are defined over the
given local source.
In order to apply this processing, a notion of consistency among topological and
cardinal directional relations has to be defined. Assume that given a topological (cardinal directional) relation θ defined over dimensions d 1 and d 2 , the set of topological
(cardinal directional) relationships defined over dimensions d 3 and d 4 which are consistent with respect to θ is denoted by r t ((d 1 , d 2 ), θ, (d 3 , d 4 )) (r c ((d 1 , d 2 ), θ, (d 3 , d 4 ))).
With those sets at hand, if d 3 is the dimension of roads and d 4 is the dimension of
towns in a local source M i , query Q 2 can be rewritten for execution against M i as
follows:
Q
i
2 = {r|r is a road, ∃θ
∈ r t ((R, R), Overlap, (d 3 , d 4 ))(∃θ
∈ r c ((R, R),
MBB:N:NE, (d 3 , d 4 ))(r θ
T 1 ∧ r θ
T 1 ))}.
In Sect. 8.6, we present two distinct consistency notions that can be used to apply
the processing described above.
8.3.4 Consistency Checking
The evaluation of consistency among a set of maps is an important issue today
since often GIS applications of different nature have to integrate and compare spatial
169
8.3.3 Query Processing in GIS Mediation Architectures
The second scenario deals with mediation systems. The basic architecture of a mediation system is based on two main components: the mediator and the wrappers. We
focus our attention on the mediator that rewrites the user’s query into local queries,
afterwards translated by the wrapper in the data source query language (see Chap. 7).
In general, mediators do not consider, in query rewriting, the possible change of
spatial relations caused by multiresolution. As an example, assume that the maps in
Fig. 8.4 represent three local sources to be integrated and that, at the global level,
features are represented with the maximal dimension by which they appear in the
local sources. In our example, this means that at the global level, roads, towns, and
pollution areas are represented as regions. Actually, in more general cases, the choice
of feature dimensions depends on the user’s application and needs; moreover, it is
possible to create specific interfaces that may impose their own feature representation
to the users.
Suppose now that the user, at the global level, wants to know the roads that
enter town T 1 from North to NorthEast. As we will see in Sect. 8.5, this query can
be specified as follows:
Q 2 = {r|r is a road, r Overlap T 1 and r MBB:N:NE T 1 }.
As predicates Overlap and MBB:N:NE may not be defined over some local
sources, such query may not return any result from some of them. For each local
source, a more reasonable approach would be that of rewriting such predicates into
a set of predicates which are consistent with the given ones and are defined over the
given local source.
In order to apply this processing, a notion of consistency among topological and
cardinal directional relations has to be defined. Assume that given a topological (cardinal directional) relation θ defined over dimensions d 1 and d 2 , the set of topological
(cardinal directional) relationships defined over dimensions d 3 and d 4 which are consistent with respect to θ is denoted by r t ((d 1 , d 2 ), θ, (d 3 , d 4 )) (r c ((d 1 , d 2 ), θ, (d 3 , d 4 ))).
With those sets at hand, if d 3 is the dimension of roads and d 4 is the dimension of
towns in a local source M i , query Q 2 can be rewritten for execution against M i as
follows:
Q
i
2 = {r|r is a road, ∃θ
∈ r t ((R, R), Overlap, (d 3 , d 4 ))(∃θ
∈ r c ((R, R),
MBB:N:NE, (d 3 , d 4 ))(r θ
T 1 ∧ r θ
T 1 ))}.
In Sect. 8.6, we present two distinct consistency notions that can be used to apply
the processing described above.
8.3.4 Consistency Checking
The evaluation of consistency among a set of maps is an important issue today
since often GIS applications of different nature have to integrate and compare spatial