A Strongly Subquadratic $(3+\varepsilon)$-Approximation for Weighted Edit Distance over Arbitrary Metrics

We study weighted edit distance between two strings of total length $n$, where edit costs are induced by an arbitrary metric. For equal-length inputs, Kuszmaul (2019) gave an $O(n^δ)$-approximation with $\widetilde{O}(n^{2-δ})$ running time for every fixed $0 < δ< 1$. We give the first constant-fact