Union of All Intersecting Sets

Question

Given a list of objects with multiple attributes I need to find the list of sets created by a union of all intersecting subsets.

Specifically these are Person object

Answer 1

To expand on my comment in the original post, you want to create a list of sets where each member of a given set shares at least one attribute with at least one other member of that set.

Naively, this can be solved either by finding all pairs that share an attribute and merging pairs together that have the same partner iteratively. This would be O(N^3) (N^2 for iterating over pairs, and up to N separate sets to determine membership).

You can also think of this problem as determining the connected component of a graph, where every object and every unique attribute value is a node; each object would be connected to each of its attribute values. Setting up that graph would take linear time, and you could determine the connected components in linear time with a breadth or depth first search.