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 Inapproximability of Generalized Linear Equations over a Finite Group
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.
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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.
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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.