Function Repository Resource:

MinimalSubsets

Prune non-minimal subsets from a list of subsets

Contributed by: Carl Woll

ResourceFunction["MinimalSubsets"][list]

prunes non-minimal subsets from the sets in list.

Details and Options

A non-minimal subset is a list which includes all elements from another subset.

The argument list should be a list of subsets, where each subset is a list of elements.

Here is a list of sets:

In[1]:=

Out[1]=

Remove the non-minimal subsets, which are {a,b,c} and {a,b,e}:

In[2]:=

Out[2]=

MinimalSubsets can handle a large list of subsets:

In[3]:=

The number of minimal subsets:

In[4]:=

Out[4]=

Uses Internal`ListMin, which is based on the BCL algorithm discussed here: https://dl.acm.org/citation.cfm?id=320196.