Need algorithm for fast storage and retrieval (search) of sets and subsets

Question

I need a way of storing sets of arbitrary size for fast query later on. I\'ll be needing to query the resulting data structure for subsets or sets that are already stored.

Answer 1

This seems like a custom made problem for a graph database. You make a node for each set or subset, and a node for each element of a set, and then you link the nodes with a relationship Contains. E.g.:

Now you put all the elements A,B,C,D,E in an index/hash table, so you can find a node in constant time in the graph. Typical performance for a query [A,B,C] will be the order of the smallest node, multiplied by the size of a typical set. E.g. to find {A,B,C] I find the order of A is one, so I look at all the sets A is in, S1, and then I check that it has all of BC, since the order of S1 is 4, I have to do a total of 4 comparisons.

A prebuilt graph database like Neo4j comes with a query language, and will give good performance. I would imagine, provided that the typical orders of your database is not large, that its performance is far superior to the algorithms based on set representations.