Abstract: A maximum constraint satisfaction problem, Max-CSP(F), is specified by a finite family of constraints F, where each constraint is of arity k. An instance of the problem on n variables is given by m applications of constraints from F to length-k subsequences of the n variables, and the goal is to find an assignment to the n variables that satisfies the maximum number of constraints. The class of Max-CSP(F) includes optimization problems such as Max-CUT, Max-DICUT, Max-3SAT, Max-q-Coloring, Unique Games, etc.
In this talk, I will present our recent dichotomy theorem on the approximability of Max-CSP(F) for every finite family F, in the single-pass dynamic streaming setting. In this setting, at each time step, a constraint is either added to or deleted from the stream. In the end, the streaming algorithm must estimate the maximum number of constraints that can be satisfied using space that is only polylogarithmic in n. No background in streaming algorithms or constraint satisfaction problems will be needed to enjoy this talk!
The talk will be based on the paper https://eccc.weizmann.ac.il/report/2021/011/, and an upcoming paper with Chi-Ning Chou, Alexander Golovnev, and Madhu Sudan.
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