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Following this trend, our idea is to combine this with a classical embedding of edit distance into the Hamming distance [10, 11] (see Section Edit distance approximation) to obtain a fuzzy keyword search for the edit distance.
(sketch of) For m,m' such that ed(m,m') > λ max, then Section Edit distance approximation implies that HD ψ(m;λ min ), ψ(m' λ min ) ≥ β log2(1/δ).
(sketch of) For m,m' such that ed(m,m') ≤ λ min, Section Edit distance approximation implies that HD ψ(m;λ min ), ψ(m' λ min ) ≤ α log2(1/δ) with probability 1 - δ. Hence P r [ f i ( ψ ( m ) ) = f i ( ψ ( m ′ ) ) ] > ( 1 - α c 2 ) r.
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