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- W3134766200 abstract "A Boolean constraint satisfaction problem (CSP), Max-CSP$(f)$, is a maximization problem specified by a constraint $f:{-1,1}^kto{0,1}$. An instance of the problem consists of $m$ constraint applications on $n$ Boolean variables, where each constraint application applies the constraint to $k$ literals chosen from the $n$ variables and their negations. The goal is to compute the maximum number of constraints that can be satisfied by a Boolean assignment to the $n$~variables. In the $(gamma,beta)$-approximation version of the problem for parameters $gamma geq beta in [0,1]$, the goal is to distinguish instances where at least $gamma$ fraction of the constraints can be satisfied from instances where at most $beta$ fraction of the constraints can be satisfied. In this work we completely characterize the approximability of all Boolean CSPs in the streaming model. Specifically, given $f$, $gamma$ and $beta$ we show that either (1) the $(gamma,beta)$-approximation version of Max-CSP$(f)$ has a probabilistic streaming algorithm using $O(log n)$ space, or (2) for every $varepsilon > 0$ the $(gamma-varepsilon,beta+varepsilon)$-approximation version of Max-CSP$(f)$ requires $Omega(sqrt{n})$ space for probabilistic streaming algorithms. Previously such a separation was known only for $k=2$. We stress that for $k=2$, there are only finitely many distinct problems to consider. Our positive results show wider applicability of bias-based algorithms used previously by [Guruswami-Velingker-Velusamy APPROX'17], [Chou-Golovnev-Velusamy FOCS'20] by giving a systematic way to explore biases. Our negative results combine the Fourier analytic methods of [Kapralov-Khanna-Sudan SODA'15], which we extend to a wider class of CSPs, with a rich collection of reductions among communication complexity problems that lie at the heart of the negative results." @default.
- W3134766200 created "2021-03-15" @default.
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- W3134766200 date "2021-01-01" @default.
- W3134766200 modified "2023-09-25" @default.
- W3134766200 title "Classification of the streaming approximability of Boolean CSPs." @default.
- W3134766200 hasPublicationYear "2021" @default.
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