Optimal Streaming Approximations for All Boolean Max 2-CSPs and Max k-SAT

Explore a 25-minute IEEE conference talk on optimal streaming approximations for Boolean Max 2-CSPs and Max k-SAT. Delve into constraint satisfaction problems in the streaming model, examining how trivial random sampling proves optimal for Max-CUT. Investigate the Max-DICUT streaming model, including a 2/5-approximation and a novel random sampling with bias approach. Analyze the relationship between total bias and cut value, and study streaming lower bounds through communication complexity. Examine the Distributional Boolean Hidden Partition (DBHP) problem and its reduction to Max-DICUT. Gain insights into future research directions in this field of computational complexity and approximation algorithms.

Syllabus

Intro
Motivation and Spoiler
Constraint Satisfaction Problem (CSP)
CSP in the Streaming Model
Trivial Random Sampling is Optimal for Max-CUT!
Max-DICUT in the Streaming Model
Warm-up: 2/5-Approximation by [GW17]
New Idea: Random Sampling with Bias
New Relation Between Total Bias and Cut Value
Streaming Lower Bounds via Communication Complexity
Distributional Boolean Hidden Partition (DBHP) Problem contains exactly
Example of DBHP (with Parallel Repetition)
Reducing DBHP to Max-DICUT (Max-2AND)
Conclusion
Future Directions