Results...

Different Data Cube generation time with different dimension, and different dimension number is given below:

These two curves are almost similar and they are linear with respect to the tuple size. And the data for the District wise Division Data line [Fig 1] is steeper than the Month wise year Data line [Fig 2]. Because Division level Hierarchy has more follower than the Year level Hierarchy. So, querying with hierarchy which is followed by more hierarchy, then the resulting line will be steeper. But both of them are linear with respect to tuple size.

These two curves are almost similar and they are linear with respect to tuple size. And the data for the District wise Division Data and smaller Range wise Range line [Fig 4] is steeper than the Data District wise Division Data and Month wise year Data line [Fig 3]. Because range hierarchy is concrete hierarchy wile Year hierarchy is a discrete hierarchy. So, Query with respect to concrete hierarchy will take more time than the discrete hierarchy.

In the Fig 5 all the curves seem to be straight line. That is all of them are linear with respect to tuple size. But the difference is the slope. Time with higher dimension has steeper line than the time with lower dimension count. And in the analysis of the algorithm we show that the slope is (number of dimension x average tuple count). So, the results support the mathematical analysis of the algorithm. Again from the analysis of the data we see that, for the fixed tuple size, time with respect to dimension number increases linearly. That also supports our mathematical analysis. So, the time is linear with respect to nay of them.

Fig 1: Cube generation time for District wise Division Data

Fig 2: Cube Generation time for Month wise Year Data

Fig 3: Cube generations time for Month wise year Data and District wise Division Data

Fig 4: Cube generations time for District wise Division Data and Smaller range wise Range Data

Fig 5: Cube generations time for different number of dimensions with different dimension value

In the Fig 6 the black line indicates the normal algorithm’s tuple vs. time relation and the cyne line indicates the hash mapped algorithm’s tuple vs. time relation, that we have developed. From the figure we found that normal algorithm is polynomial. We also found that our developed algorithm is linear.

Fig 6: Time comparison between normal and hash mapped algorithm

Here is the result of the space required to hold the data cube. In the Fig 7 we see the graph is almost linear, hence the space required is linear with respect to tuple size. This line cut the X-axis, but in reality the size will be fixed at 8KB, which is the block size of windows file system.

Fig 7: Transaction Table size vs Space required