
Approximability of all Boolean CSPs in the dynamic streaming setting
A Boolean constraint satisfaction problem (CSP), MaxCSP(f), is a maximi...
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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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Linear Space Streaming Lower Bounds for Approximating CSPs
We consider the approximability of constraint satisfaction problems in t...
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A dichotomy theorem for nonuniform CSPs simplified
In a nonuniform Constraint Satisfaction problem CSP(G), where G is a se...
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On Approximating Partial Set Cover and Generalizations
Partial Set Cover (PSC) is a generalization of the wellstudied Set Cove...
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Hermitian Laplacians and a Cheeger inequality for the Max2Lin problem
We study spectral approaches for the MAX2LIN(k) problem, in which we a...
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Practical implementation of a quantum backtracking algorithm
In previous work, Montanaro presented a method to obtain quantum speedup...
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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 finite set of constraints F⊆{[q]^k →{0,1}} for positive integers q and k. An instance of the problem on n variables is given by m applications of constraints from F to subsequences of the n variables, and the goal is to find an assignment to the variables that satisfies the maximum number of constraints. In the (γ,β)approximation version of the problem for parameters 0 ≤β < γ≤ 1, the goal is to distinguish instances where at least γ fraction of the constraints can be satisfied from instances where at most β fraction of the constraints can be satisfied. In this work we consider the approximability of this problem in the context of streaming algorithms and give a dichotomy result in the dynamic setting, where constraints can be inserted or deleted. Specifically, for every family F and every β < γ, we show that either the approximation problem is solvable with polylogarithmic space in the dynamic setting, or not solvable with o(√(n)) space. We also establish tight inapproximability results for a broad subclass in the streaming insertiononly setting. Our work builds on, and significantly extends previous work by the authors who consider the special case of Boolean variables (q=2), singleton families ( F = 1) and where constraints may be placed on variables or their negations. Our framework extends nontrivially the previous work allowing us to appeal to richer norm estimation algorithms to get our algorithmic results. For our negative results we introduce new variants of the communication problems studied in the previous work, build new reductions for these problems, and extend the technical parts of previous works.
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