1. Beyond Set Disjointness: The Communication Complexity of Finding the Intersection Grigory Yaroslavtsev http://grigory.us Joint with Brody, Chakrabarti, Kondapally and Woodruff

2. Communication Complexity [Yao’79] Shared randomness …

3. Set Intersection

4. Our results {

5. Applications

7. Hashing Expected # of elements

8. Secondary Hashing

10. Collisions

13. Main protocol Expected # of elements

14. Verification tree …

15. Verification bottom-up

16. EQUALITY CHECK Verification bottom-up Correct Incorrect Correct Incorrect

17. Correct Verification bottom-up Correct Incorrect EQUALITY CHECK FAILS => RESTART THE SUBTREE Correct Incorrect Correct

18. Verification bottom-up … … …

20. Multi-party extensions

21. Open Problems