2-party private set intersection
Here are some recent papers that explicitly study optimizing PSI for the case of unequal set sizes.


Private Set Intersection for Unequal Set Sizes with Mobile Applications; Ágnes Kiss, Jian Liu, Thomas Schneider, N. Asokan, Benny Pinkas
Fast Private Set Intersection from Homomorphic Encryption; Hao Chen, Kim Laine, Peter Rindal
Unbalanced Approximate Private Set Intersection; Amanda Cristina Davi Resende, Diego F. Aranha


Update:


PIR-PSI: Scaling Private Contact Discovery; Daniel Demmler, Peter Rindal, Mike Rosulek, Ni Trieu