
Optimal Streaming Approximations for all Boolean Max2CSPs
We prove tight upper and lower bounds on approximation ratios of all Boo...
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Streaming approximation resistance of every ordering CSP
An ordering constraint satisfaction problem (OCSP) is given by a positiv...
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Max3Lin over NonAbelian Groups with Universal Factor Graphs
Factor graph of an instance of a constraint satisfaction problem with n ...
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Approximability of all finite CSPs in the dynamic streaming setting
A constraint satisfaction problem (CSP), MaxCSP( F), is specified by a ...
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An Optimal Space Lower Bound for Approximating MAXCUT
We consider the problem of estimating the value of MAXCUT in a graph in...
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Improving the Integrality Gap for Multiway Cut
In the multiway cut problem, we are given an undirected graph with nonn...
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Consistency and Random Constraint Satisfaction Models
In this paper, we study the possibility of designing nontrivial random ...
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Linear Space Streaming Lower Bounds for Approximating CSPs
We consider the approximability of constraint satisfaction problems in the streaming setting. For every constraint satisfaction problem (CSP) on n variables taking values in {0,…,q1}, we prove that improving over the trivial approximability by a factor of q requires Ω(n) space even on instances with O(n) constraints. We also identify a broad subclass of problems for which any improvement over the trivial approximability requires Ω(n) space. The key technical core is an optimal, q^(k1)inapproximability for the case where every constraint is given by a system of k1 linear equations q over k variables. Prior to our work, no such hardness was known for an approximation factor less than 1/2 for any CSP. Our work builds on and extends the work of Kapralov and Krachun (Proc. STOC 2019) who showed a linear lower bound on any nontrivial approximation of the max cut in graphs. This corresponds roughly to the case of Max kLINq with k=q=2. Each one of the extensions provides nontrivial technical challenges that we overcome in this work.
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