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. 
REFERENCES 
Bebel, B., Królikowski, Z. and Wrembel, R., 2006. 
Managing evolution of data warehouses by means of 
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Blaschka, M., Sapia, C. and Höfling, G., 1999. On schema 
evolution in multidimensional databases. In Data 
Warehousing and Knowledge Discovery(pp. 153-164). 
Springer Berlin Heidelberg. 
Body, M., Miquel, M., Bédard, Y. and Tchounikine, A., 
2003, March. Handling evolutions in multidimensional 
structures. In Data Engineering, 2003. Proceedings. 
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