1. 1 Exercise Sheet 3 Exercise 7.: ROLAP Algebra Assume that a fact table SalesCube has 3 hierarchies with attributes  ear , Month M, Productgroup P and City C and the measure sales. Assume that the attributes have the following cardinalities:  = 3 M = 12 P = 500 C = 80 Exercise 7.1: Draw the aggregation network

2. 2 Exercise 7.2.: Construct the ROLAP expression to compute the average and maximal sales for the groups { ,P}, { , C} and {P} Exercise 7.3: Translate the ROLAP expression of Exercise 7.2 into a single SQL statement and estimate its cost = total number of tuples read + total number of tuples written if you assume that there is no optimization of this SQL statement. Exercise 7.4: Translate the SQL statement of Exercise 7.3 into several SQL statements employing auxiliary tables for intermediate results. Try to minimize the cost.

3. 3 Exercise 8: Clustering Exercise 8.1: Compute the NN distances for the following set of points and label the corresponding edges. A * D * BC * Exercise 8.2: Compute the natural nearest neighbor distances for the points of Exercise 8.1

4. 4 Exercise 8.3: Draw the minimal spanning tree for the following set of points EF G CD B A H I J Exercise 8.4: Which clusters result, if we want to have 2 clusters, 4 clusters, 5 clusters?

5. 5 Exercise 8.5: Which clusters result from the k-means algorithm if we use the small circles as starting centroids for the clusters? EF G CoDo B A H I o oJ