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Efficient Algorithms and New Characterizations for CSP Sparsification by Khanna, Sanjeev; Putterman, Aaron L.; Sudan, Madhu is a scholarly article available to read on EtoBox.

What is Efficient Algorithms and New Characterizations for CSP Sparsification about?

CSP sparsification, introduced by Kogan and Krauthgamer (ITCS 2015), considers the following question: how much can an instance of a constraint satisfaction problem be sparsified (by retaining a reweighted subset of the constraints) while still roughly capturing the weight of constraints satisfied by {\em every} assignment. CSP sparsification captures as a special case several well-studied problems including graph cut-sparsification, hypergraph cut-sparsification, hypergraph XOR-sparsification, and corresponds to a general class of hypergraph sparsification problems where an arbitrary $0/1$-valued {\em splitting function} is used to define the notion of cutting a hyperedge (see, for instance, Veldt-Benson-Kleinberg SIAM Review 2022). The main question here is to understand, for a given constraint predicate $P:\Sigma^r \to \{0,1\}$ (where variables are assigned values in $\Sigma$), the smallest constant $c$ such that $\widetilde{O}(n^c)$ sized sparsifiers exist for every instance of a constraint satisfaction problem over $P$. A recent work of Khanna, Putterman and Sudan (SODA 2024) [KPS24] showed {\em existence} of near-linear size sparsifiers for new classes of CSPs. In this work (

Author

Khanna, Sanjeev; Putterman, Aaron L.; Sudan, Madhu

Published

2024

Language

EN