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Hardness of Approximate Nearest Neighbor Search under L-infinity
[article]
2020
arXiv
pre-print
We show conditional hardness of Approximate Nearest Neighbor Search (ANN) under the ℓ_∞ norm with two simple reductions. Our first reduction shows that hardness of a special case of the Shortest Vector Problem (SVP), which captures many provably hard instances of SVP, implies a lower bound for ANN with polynomial preprocessing time under the same norm. Combined with a recent quantitative hardness result on SVP under ℓ_∞ (Bennett et al., FOCS 2017), our reduction implies that finding a
arXiv:2011.06135v1
fatcat:n4ywphahqnfqbf35gri33pj774