For any CSP predicate R, unweighted CSP(R) instances admit sparsifiers of size at most their non-redundancy (up to polylog factors); weighted cases are pinned to chain length, via a VC-type theorem for set families using the entropy method.
A constant lower bound for the union- closed sets conjecture
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Chain length characterizes multiplicative sparsifiability of set systems, shown via a generalized contraction algorithm that simplifies earlier proofs.
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Redundancy Is All You Need (for CSP Sparsification)
For any CSP predicate R, unweighted CSP(R) instances admit sparsifiers of size at most their non-redundancy (up to polylog factors); weighted cases are pinned to chain length, via a VC-type theorem for set families using the entropy method.
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Multiplicative error set system sparsification: A simpler proof via chain length contraction
Chain length characterizes multiplicative sparsifiability of set systems, shown via a generalized contraction algorithm that simplifies earlier proofs.