Proves detection of RGG vs. ER is impossible for d ≫ (n h(p))^3 and d ≥ (1+ε)n, resolving the detection threshold conjecture in the regime p ≳ n^{-2/3}/log n.
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2026 3verdicts
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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.
citing papers explorer
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Resolution of the Detection Threshold Conjecture for Random Geometric Graphs in the $d>n$ Regime
Proves detection of RGG vs. ER is impossible for d ≫ (n h(p))^3 and d ≥ (1+ε)n, resolving the detection threshold conjecture in the regime p ≳ n^{-2/3}/log n.
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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.