The Simple Assignment provides the fastest possible partitioning method that uses the smallest amount of memory. The vertices are assigned to the partitions simply corresponding to their vertex numbers. Assume a mesh with 1000 vertices that has to be partitioned into 10 partitions. The Simple Assignment produces the following partitions:

Partition 1:        Vertices 1-100
Partition 2:        Vertices 101-200
Partition 3:        Vertices 201-300
...

This is reasonable for hex meshes because their vertices are generally in topological order. However, this partitioning method can be arbitrarily bad for unstructured meshes and can result in huge overlapping regions.