Find smallest subset prefixes
The best solution I have for this. If my understanding is good, this is a fairly simple to solve and you do not need anything else than a set.

There might be a better way than rebuilding entirely the set.

words = ['foo', 'foog', 'food', 'asdf']
prefixes = set()

for w in words:
    if any(p for p in prefixes if w.startswith(p)):
        # A prefix exists in the prefixes set.
        continue

    # Re-build the set with all elements not matching the set.
    prefixes = set(p for p in prefixes if not p.startswith(w))
    prefixes.add(w)

print(prefixes)