Non-adaptive LCAs for constant approximations of matching and vertex cover require Δ^{Ω(log Δ / log log Δ)} queries, so the Parnas-Ron black-box reduction is optimal up to exponents.
Sp ace-Efficient Local Computation Algorithms
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Lower Bounds for Non-adaptive Local Computation Algorithms
Non-adaptive LCAs for constant approximations of matching and vertex cover require Δ^{Ω(log Δ / log log Δ)} queries, so the Parnas-Ron black-box reduction is optimal up to exponents.