A reduction framework from sample complexity yields matching time lower bounds for purity estimation, high-order functionals, productness testing, and related quantum protocols.
[Mar10] D´ aniel Marx
5 Pith papers cite this work. Polarity classification is still indexing.
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2026 5representative citing papers
Under ETH, no f(k) n^{o(k/log k)}-time algorithm can approximate k-permutation pattern counts within n^{(1/2-ε)k} factor, matching exact-counting hardness.
Uniform-Ironed-Virtual-Value Item Pricing achieves a tight 3-approximation to the Duality Relaxation Benchmark in unit-demand single-buyer revenue maximization.
A new algorithm approximates the prize-collecting rural postman problem within a factor strictly less than 1.6 and proves a 2-approximation barrier for PCTSP reductions.
Reduction from prize-collecting-Φ-TSP to prize-collecting TSP yields (ρ + ε)-approximations for constant prescribed vertices, improving the prize-collecting stroll guarantee to better than 1.6 from 1.6662.
citing papers explorer
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Quantum Time Lower Bounds by Permutation Invariance
A reduction framework from sample complexity yields matching time lower bounds for purity estimation, high-order functionals, productness testing, and related quantum protocols.
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Inapproximability of Counting Permutation Patterns
Under ETH, no f(k) n^{o(k/log k)}-time algorithm can approximate k-permutation pattern counts within n^{(1/2-ε)k} factor, matching exact-counting hardness.
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Benchmark-Tight Approximation Ratio of Simple Mechanism for a Unit-Demand Buyer
Uniform-Ironed-Virtual-Value Item Pricing achieves a tight 3-approximation to the Duality Relaxation Benchmark in unit-demand single-buyer revenue maximization.
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Approximation algorithms for the prize-collecting rural postman problem
A new algorithm approximates the prize-collecting rural postman problem within a factor strictly less than 1.6 and proves a 2-approximation barrier for PCTSP reductions.
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Reducing Prize-Collecting Stroll and Related Routing Problems to Prize-Collecting TSP
Reduction from prize-collecting-Φ-TSP to prize-collecting TSP yields (ρ + ε)-approximations for constant prescribed vertices, improving the prize-collecting stroll guarantee to better than 1.6 from 1.6662.