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smaller than a class at the lower end. This is because, generally, one complex
(collection) object utilizes multiple “part” objects (that could be from the same
or different classes).
As a result, the organization of classes within the schema graph has its influ-
ence on the distribution of both the number and size of objects among the classes
of the database. To reflect this notion statistically, every hierarchy was divided into
four quarters (starting with the lowest quarter) and assigned a varying percentage
of the number of objects of various sizes to the classes of that quarter. Therefore,
a percentage distribution takes the form of a vector with 4 entries ([low quarter,
mid_low quarter, mid_high quarter, high quarter]). The simulator assumed an av-
erage of eight classes for each hierarchy and categorized the sizes of objects as
small, medium, large and very large—a percentage distribution of object sizes of
[VL , L , M , S] means that the lowest quarter of classes along the hierarchy contains
very large objects, whereas the highest quarter contains small objects. Similarly a
percentage distribution of the cardinality of classes that equals [34,25,18,9] means
that 40% of the objects within the database are found within the lowest quarter
classes, 30% in the higher hierarchy and so on. A small object is a textual-based
security price of size 16 bytes. A very large (non-complex) object can be a ( 2 × 3 ) -
inch graph that contains 16 colors. Such an object would require 6K bytes. Finally,
the size of the index structure is dependent on the number of distinct keys for the
objects within a class. It was assumed that 60% of the objects have distinct keys and
that the value of any attribute is uniformly distributed among the objects contain-
ing such attribute. Table IV shows a list of all the input parameters assumed for this
case.
For these simulation runs, the information along the broadcast channel is orga-
nized in four different fashions: the hierarchical and single-class methods for the
inheritance and aggregation relationships. Note that it is the number of objects (not
data pages) that controls the number of index blocks. For example, the number of
data pages of the inheritance case is about 2.5 times more than that of the aggrega-
tion case. However, the number of the index blocks is equivalent since the number of
the objects in both cases is the same. Within each indexing scheme, for each query,
the simulator simulates the process of probing the air channel, getting the required
index pages, and retrieving the required data pages. In each query, on average, two
objects from each class are retrieved. The simulation measures the response time and
amount of energy consumed.
6.1.3.1 Response Time. Placing an index along the air channel con-
tributes to extra storage overhead and thus longer response time. Therefore, the best
response time is achieved when no index is placed on the broadcast, and the entire
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