Algorithm for commonalities across related objects

I am making early forays into the application of algorithms to best solve a problem and I am finding it difficult to choose the best application.

The problem is give the data below (two columns) find those ids where the linkedId matches entirely:

Input

id  linkedId
1   103
2   107
1   107
2   103
4   64
6   120
7   107
8   180
7   64
9   129


Expected output [1,2] as the linkedIds match entirely for the two ids

As I look at the data, I would envisage a graph of some description so that I can establish the various links between the ids and linkedIds but I am at a loss as to how to approach this.

I do not want a solution but more guiding in the right direction.

Thanks

• By “matched exactly” what do you mean? Do you mean that the set of linkedIds that each id in the output maps to are exactly the same? What if there are two sets of ids in the input such that each set of ids maps to the same linkedIDs within a set but not across sets, should we return them then? In other words, are we looking for all Ids such that there exists another ID with the exact same mapped set of linkedIds? – Throckmorton Apr 21 '19 at 0:31

1. During input, create a table for each id, record all the linkedId of it, and the sum of linkedIds of it.
2. After recording all the input, you have tons of ways to find those ids whose sum of all linkedIds are the same, put them into groups, like an $$O(n^2)$$ brute-force or some $$O(n\log(n))$$ discretization. This step is a kind of classification, all ids in a group may not be the equivalent, but equivalent ids must be in the same group
3. Traverse through all groups, find those equivalent ids