Difference between HEM & SHEM

I am not sure to understand how works the Sorted Heavy Edge Matching (SHEM) in kmetis and pmetis.
Is it like the modified Heavy Edge Matching (HEM*) as described in [1] ? Is it a determinist version of the Heavy Edge Matching (HEM) ? Or is it something else ?

Thanks in advance.


[1] 1998. Multilevel k-way Partitioning Scheme for Irregular Graphs. George Karypis and Vipin Kumar. J. Parallel Distrib. Comput. 48(1): 96-129, 1998.

RE: SHEM is not the HEM*. It is

SHEM is not the HEM*. It is just like HEM, but the edges are visited in a somewhat global sorted order based on their weights.