Well, considering you have made your choice of using MongoDB, you will have to maintain multiple collections. One is your main collection, and you will have to maintain user specific collections which hold user data, say the document ids the user has swiped. Then, when you want to fetch data, you might want to do a setDifference aggregation. SetDifference does this:
Takes two sets and returns an array containing the elements that only
exist in the first set; i.e. performs a relative complement of the
second set relative to the first.
Now how performant this is would depend on the size of your sets and the overall scale.
EDIT
I agree with your comment that this is not a scalable solution.
Solution 2:
One solution I could think of is to use a graph based solution, like Neo4j. You could represent all your 1M objects and all your user objects as nodes and have relationships between users and objects that he has swiped. Your query would be to return a list of all objects the user is not connected to.
You cannot shard a graph, which brings up scaling challenges. Graph based solutions require that the entire graph be in memory. So the feasibility of this solution depends on you.
Solution 3:
Use MySQL. Have 2 tables, one being the objects table and the other being (uid-viewed_object) mapping. A join would solve your problem. Joins work well for the longest time, till you hit a scale. So I don't think is a bad starting point.
Solution 4:
Use Bloom filters. Your problem eventually boils down to a set membership problem. Give a set of ids, check if its part of another set. A Bloom filter is a probabilistic data structure which answers set membership. They are super small and super efficient. But ya, its probabilistic though, false negatives will never happen, but false positives can. So thats a trade off. Check out this for how its used : http://blog.vawter.com/2016/03/17/Using-Bloomfilters-to-Avoid-Repetition/
Ill update the answer if I can think of something else.