Consider the execution of a MapReduce algorithm on a cluster with 10machines, each equipped with a RAM of 8 GB and a disk of 128 GB. Before and afterthe Map and Reduce Phases of each round, data are stored into a HDFS built on theunion of the disks. Let ML and MA be the algorithm’s local and aggregate space.What are the maximum values (in GB) for ML and MA which ensure a successfulexecution of the algorithm?

The MapReduce algorithm operates in two main phases: the Map phase and the Reduce phase.

1. Map Phase: In this phase, the input dataset is divided into independent chunks which are processed by the map tasks in a completely parallel manner. The framework sorts the outputs of the maps.

2. Reduce Phase: In this phase, the sorted output from the map phase is given as input. The framework then calls the Reduce function for each unique key in the sorted order.

Now, let's calculate the maximum values for ML (local space) and MA (aggregate space).

1. ML (Local Space): This is the maximum amount of data that can be stored on a single machine. Since each machine has a RAM of 8 GB and a disk of 128 GB, the maximum local space ML is the sum of these two, which is 136 GB.

2. MA (Aggregate Space): This is the total amount of data that can be stored across all machines in the cluster. Since there are 10 machines, each with a disk of 128 GB, the maximum aggregate space MA is 10 * 128 GB, which is 1280 GB.

So, the maximum values for ML and MA which ensure a successful execution of the algorithm are 136 GB and 1280 GB respectively.