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What's immediate superset?

Why is it called immediate?

They appear in the context of Apriori algorithm. Particularly the one enhanced with hashing.

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  • $\begingroup$ If my answer helped you, please consider accepting to mark the question as answered. $\endgroup$ – n1k31t4 Jun 13 '18 at 21:15
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Immediate often occurs simply to say that there are perhaps many supersets, e.g. when we have a tree like structure. There is also for example, the converse, an immediate subset.


Example

Set A has a superset B, and that superset has its own superset C. In this case, A must also be contained within C, but the set B lies within that realm and so is the immedaite superset of A.

Perhaps it is best visualised with a Venn diagram, where B is the immediate superset of A and equally the immediate subset of C:

enter image description here


There is some discussion here on Cross-Validated too, where the selected answer shows some further usage of the term (albeit in a slightly different context). Have a look at this source for some usage of the term, which leads you to my understanding.

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  • $\begingroup$ And it's specifically called immediate, rather than intermediate? Or does it always refer to the "next" or "previous", if there are more sets between? $\endgroup$ – mavavilj May 21 '18 at 6:49
  • $\begingroup$ At this point I personally would be just considering the linguistic connotation of the situation. Immediate means 'next to' and intermediate would mean 'between'. For example, if set D was the immediate superset of C, there would be several intermediate sets between e.g. A and D... Namely sets B and C. Does that help? $\endgroup$ – n1k31t4 May 21 '18 at 10:16
  • $\begingroup$ The use of the term immediate still seems a bit odd. It could mean e.g. the superset that contains "fewest additional sets". $\endgroup$ – mavavilj Jun 29 '18 at 19:32
  • $\begingroup$ I guess it could mean a great many things, depending on the context. Your suggestion seems to be a generalisation of my concret example. I would suggest to explain it very well whenever you use it yourself to save people this confusion! $\endgroup$ – n1k31t4 Jun 29 '18 at 19:42

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