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Settling the Approximation Ratio of Boolean Max-2CSP in the Streaming Model

Speaker: Santhoshini and Chi-Ning
Title: Settling the Approximation Ratio of Boolean Max-2CSP in the Streaming Model
Date: 03 Feb 2020 5:30pm-7:00pm
Location: Maxwell-Dworkin 221
Food: Indian

Abstract: Constraint Satisfaction Problem (CSP)is one of the central computational problems studied in complexity theory. In this work,we focus on the streaming model where the input is a sequence of constraints and the goal is to approximate the maximum number of satisfied constraints using space as small as possible.

Unlike the traditional setting,there have been very few results in the streaming model. A recent line of works culminating in [Kapralov-Krachun, STOC 2019]shows that $(1/2+\epsilon)$-approximation for Max-CUT requires $\Omega(n)$ space while there is a trivial 1/2-approximation using $O(\log n)$ space. However,the knowledge of the right approximation ratio for other boolean 2CSP in the streaming model remain elusive. Specifically,prior to this work,there is a 2/5-approximation for Max-DICUT while the hardness side only refutes 1/2-approximation [Guruswami-Velingker-Velusamy, APPROX-RANDOM 2017].

In this work,we show that,surprisingly,the right approximation ratio for Max-DICUT in the streaming model is 4/9. Furthermore,we settle down the right approximation ratios for all the boolean 2CSP in the streaming model. The techniques we are using are random samplings and reductions from the distributional implicit hidden matching problem (DIHP).

This is a joint work with Sasha Golonev.