Gives an approximation algorithm for satisfiable instances of generalized linear equation CSPs over finite groups that is optimal for certain S, while the predicate remains approximation resistant on almost-satisfiable instances.
Computational Complexity , volume=
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An efficient algorithm recovers phylogenetic trees from Θ(n) noisy quartets under random classification noise, matching the information-theoretic lower bound and achieving near-optimal quartet distance.
Triplet constraints realizable in D-dimensional Euclidean space cannot be preserved above 50% accuracy by any embedding of dimension at most cD for constant c<1, with UGC-hardness preventing better polynomial-time solutions in any dimension.
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Optimal Phylogenetic Reconstruction from Sampled Quartets
An efficient algorithm recovers phylogenetic trees from Θ(n) noisy quartets under random classification noise, matching the information-theoretic lower bound and achieving near-optimal quartet distance.
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Provable Accuracy Collapse in Embedding-Based Representations under Dimensionality Mismatch
Triplet constraints realizable in D-dimensional Euclidean space cannot be preserved above 50% accuracy by any embedding of dimension at most cD for constant c<1, with UGC-hardness preventing better polynomial-time solutions in any dimension.