Preference1 :If WAvail[i,1]=1 and
HAwail[i,1]=1 then message is WS
1
V
i
and
HS
1
V
i
, 1≤i≤ n
Preference2 :If WAvail[i,1]=1 and
HAwail[j,1]=1 then message is WS
1
V
i
and
HS
1
V
j,
1≤i≤n, 1≤j≤ n, i് j
Preference3 :If WAvail[i,1]=1 and
HAwail[i,k]=1 then message is WS
1
V
i
and
HS
k
V
i
,1≤i≤n, 2≤k≤6
If WAvail[i,k]=1 and HAwail[i,1]=1
then message is WS
k
V
i
and HS
1
V
i
,1≤i≤n,
2≤k≤5
Preference4 :If matrices WAvailand
HAvail are all zeroes then the message
is ‘what’ term and 'how' ‘are not
available’
If matrix WAvail is all zeroes and if
HAvail[i,k]=1 for 1≤k≤5 then the
message is ‘what’ term ‘is not
available’ and HS
k
V
i,
1≤i≤n
If matrix HAvail is all zeroes and and
if WAvail[i,k]=1 for 1≤k≤6 then the
message is ‘how’ term ‘is not
available’ andWS
k
V
i,
1≤i≤n
4.2.3 Time Complexity of DSA
DSA algorithm scans and compares the attributes of
the latest E-Metadata version and the DO entries
once. The number of comparisons is the number of
attributes in the latest E-Metadata (say m) + no. of
entries in the Delta Ontology (say k). Therefore,
complexity= O (m+k)
In order to analyze the complexity, we compare it
with the complexity of an algorithm in the absence
of DO. In this case, an algorithm to find ‘what’ and
‘how’ terms, would have to scan and compare each
attribute of each and every version of E-Metadata.
Therefore,
Complexity = average no. of attributes in a E-
Metadata version (m) * number of E-Metadata
versions (n)
= O (m*n)
Let us analyze n and k.
Case1: If k is very large and is equal (n-1)*m then
the complexity of DSA is the same as complete scan
algorithm.
Case 2: If k << (n-1)*m then the complexity DSA is
much lower.
Case 1 will occur if the number of changes is as high
as the E-Metadata itself. This is a highly unlikely
scenario. Case 2 will occur most of the time.
It must be noted that in both the cases matrices
have to be built to give the complete picture to the
user and further, the time taken to scan the matrices
would be the same for both the algorithms.
5 CONCLUSION
The aim is to find whether the multiple warehouse
versions cater to the needs of the business user. The
needs are expressed using ‘what’ and ‘how’ terms.
These may be business terms and not necessarily
schema terms. We have built Delta Ontology to
capture the mapping between business terms and
schema terms. The Delta Ontology itself is built
using the differences in the metadata of the
warehouse schema as it undergoes changes. All the
versions where the terms are available is picked up
and listed according to the preference order.
Java is used for building the prototype of the
system and SQL Server 2005 is used as back end
tool to store metadata of the warehouse.
It may be argued that special data structures for
sparse matrices can be used to store the contents of
WAvail and HAvail. Since the matrices are not very
large the time taken to scan them is not very high.
As far as populating them is concerned, DSA is
better in terms of time complexity than complete
scan of all versions.
It may be noted that we have not defined a query
language to query multi versions of the metadata.
Query language is appropriate when different ad hoc
queries are to be framed. In our case, we search only
for ‘what’ and ‘how’ terms. Therefore, an
appropriate GUI is built to accept these terms.
In our system, it is possible for the user to know
whether the missing information in the current
schema was available in an earlier version or not.
This, we believe, will help the user decide whether
or not to change the current data warehouse schema.
It is, also, possible to see whether earlier versions
were more in tune to the decision maker’s needs. It
will also give a feedback on the evolution of the
schema vis-a-vis it satisfying query needs.
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Bebel, B., Królikowski, Z. and Wrembel, R., 2006.
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Blaschka, M., Sapia, C. and Höfling, G., 1999. On schema
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Body, M., Miquel, M., Bédard, Y. and Tchounikine, A.,
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