  Weighted minwise hashing is a standard dimensionality reduction technique
with applications to similarity search and large-scale kernel machines. We
introduce a simple algorithm that takes a weighted set $x \in \mathbb{R}_{\geq
0}^{d}$ and computes $k$ independent minhashes in expected time $O(k \log k +
\Vert x \Vert_{0}\log( \Vert x \Vert_1 + 1/\Vert x \Vert_1))$, improving upon
the state-of-the-art BagMinHash algorithm (KDD '18) and representing the
fastest weighted minhash algorithm for sparse data. Our experiments show
running times that scale better with $k$ and $\Vert x \Vert_0$ compared to ICWS
(ICDM '10) and BagMinhash, obtaining $10$x speedups in common use cases. Our
approach also gives rise to a technique for computing fully independent
locality-sensitive hash values for $(L, K)$-parameterized approximate near
neighbor search under weighted Jaccard similarity in optimal expected time
$O(LK + \Vert x \Vert_0)$, improving on prior work even in the case of
unweighted sets.
