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How to Fix a Broken Metric: A Linear Kernel, Tight Bounds, and Tree Metrics
Given a complete graph whose edge weights represent dissimilarities, Metric Violation Distance asks whether at most $k$ weights can be changed to form a metric. Motivated by metric repair for noisy data, the problem admits a polynomial-time $O(\log n)$-approximation due to Cohen-Addad, Fan, Lee and
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