8 Using Qualitative Information in Query Proc. over Multiresolution Maps
161
3. Consistency Checking. In order to compare or use together multiresolution maps
in processing activities, tools for consistency analysis of data sets obtained from
different sources are required in order to establish whether maps may lead to
contradictory results if a user performs some kind of analysis over them.
In all the contexts presented above, the specification of equality-based queries
and consistency checking methods—by which the user specifies in an exact way the
constraints that data to be retrieved or to be checked must satisfy—may not be the
right choice as multiresolution is not effectively used during such processing. In order to exploit multiresolution, a possible approach would be that of introducing some
mechanism of query relaxation, by which the specific characteristics of multiresolution maps are taken into account and, as a consequence, approximated answers are
returned to the user. This approach may generate some false hits but at the same time
makes query answers more satisfactory from the user point of view.
In this chapter, we tackle this problem by discussing some qualitative techniques
for query relaxation over geographical maps. Here “qualitative” means that we rely
on the use of spatial relationships. More precisely, we restrict ourselves to consider
topological and cardinal spatial relationships, due to their importance in real applications. Under this assumption, relaxation can be defined by introducing some distance
functions for topological and cardinal directional relationships. Such functions can
then be used in similarity-based query processing, to relax spatial predicates specified in the user query, and in mediator query processing to detect the closest predicates to the global one, in each local source. We notice that spatial relations are a
good choice for also checking map consistency. Indeed, even if both geometry and
properties concerning spatial relationships are available in a multiresolution map, it
seems reasonable to discard geometry. Indeed, geometric consistency would be reduced to an equality test between two geometric map representations and similarity
will require a sort of object extension measure in order to compare the geometric
changes between two objects; in both cases, after a change of resolution (i.e. dimension), these properties cannot be preserved. On the other hand, map representations
based on spatial relationships seem more suitable for checking consistency. Indeed,
information about spatial relationships is more abstract than the geometric one and
describes properties that are preserved after object dimension changes.
We remark that, despite a lot of work already exists concerning multiresolution
modeling and spatial relations (see Sect. 8.2), only a few approaches directly exploit
spatial relations combined with multiresolution in query processing. In particular,
existing distance functions for spatial relationships are defined over pairs of objects
with fixed dimension; thus they cannot be directly applied to multiresolution maps.
The aim of this chapter is therefore to: (i) provide a model for topological and
cardinal directional relationships in multiresolution spatial data sets, suitable for
defining relaxed query processing techniques; (ii) extend existing distance functions
for topological and cardinal directional relationships; (iii) use distance functions for
checking consistency of multiresolution spatial data sets; (iv) present examples about
how the previous concepts can be used for spatial query processing in a distributed
environment.
161
3. Consistency Checking. In order to compare or use together multiresolution maps
in processing activities, tools for consistency analysis of data sets obtained from
different sources are required in order to establish whether maps may lead to
contradictory results if a user performs some kind of analysis over them.
In all the contexts presented above, the specification of equality-based queries
and consistency checking methods—by which the user specifies in an exact way the
constraints that data to be retrieved or to be checked must satisfy—may not be the
right choice as multiresolution is not effectively used during such processing. In order to exploit multiresolution, a possible approach would be that of introducing some
mechanism of query relaxation, by which the specific characteristics of multiresolution maps are taken into account and, as a consequence, approximated answers are
returned to the user. This approach may generate some false hits but at the same time
makes query answers more satisfactory from the user point of view.
In this chapter, we tackle this problem by discussing some qualitative techniques
for query relaxation over geographical maps. Here “qualitative” means that we rely
on the use of spatial relationships. More precisely, we restrict ourselves to consider
topological and cardinal spatial relationships, due to their importance in real applications. Under this assumption, relaxation can be defined by introducing some distance
functions for topological and cardinal directional relationships. Such functions can
then be used in similarity-based query processing, to relax spatial predicates specified in the user query, and in mediator query processing to detect the closest predicates to the global one, in each local source. We notice that spatial relations are a
good choice for also checking map consistency. Indeed, even if both geometry and
properties concerning spatial relationships are available in a multiresolution map, it
seems reasonable to discard geometry. Indeed, geometric consistency would be reduced to an equality test between two geometric map representations and similarity
will require a sort of object extension measure in order to compare the geometric
changes between two objects; in both cases, after a change of resolution (i.e. dimension), these properties cannot be preserved. On the other hand, map representations
based on spatial relationships seem more suitable for checking consistency. Indeed,
information about spatial relationships is more abstract than the geometric one and
describes properties that are preserved after object dimension changes.
We remark that, despite a lot of work already exists concerning multiresolution
modeling and spatial relations (see Sect. 8.2), only a few approaches directly exploit
spatial relations combined with multiresolution in query processing. In particular,
existing distance functions for spatial relationships are defined over pairs of objects
with fixed dimension; thus they cannot be directly applied to multiresolution maps.
The aim of this chapter is therefore to: (i) provide a model for topological and
cardinal directional relationships in multiresolution spatial data sets, suitable for
defining relaxed query processing techniques; (ii) extend existing distance functions
for topological and cardinal directional relationships; (iii) use distance functions for
checking consistency of multiresolution spatial data sets; (iv) present examples about
how the previous concepts can be used for spatial query processing in a distributed
environment.