1. Matrix multiplication. A lot of real life problems can be solved via a linear algebra approach. Among the many parallel  algorithms for matrix multiplication, Fox’s Algorithm and Cannon’s Algorithm perform the best. With column/row decomposition strategy we are able to process such approaches via map-reduce.

2. After translating a real life problem into matrices we are able to cluster the related data. I.e. Kmeans clustering is a well-known clustering algorithm aiming to cluster a set of data points to a predefined number of clusters. More details of this analysis can be found in this paper

3. Beside the clustering of unstructured data we have to form groups. More details of this analysis can be found in this paper.

4. Counting. This is a simple MapReduce computation that is often use to explain the MapReduce programming model. Very very basic but important. 

5. Filtering. As basic as counting but most time not considered. Drop out unnecessary data.