Parallel algorithm for matroid basis computation with O(n^{1/3} log^{1/3} n) round complexity, nearly matching the KUW lower bound.
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Liu, Richard Peng, Maximilian Probst Gutenberg, and Sushant Sachdeva
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A threshold κ=Θ(1/√α) (α=m/n) separates easy collision finding from OGP-based exponential lower bounds against online algorithms in single-layer binary NNs.
First deterministic sublogarithmic-round spanner and APSP algorithms in linear, sublinear, and near-linear MPC plus Congested Clique via derandomized hitting sets.
The first dynamic algorithms for matrix rank and related objects achieve update times scaling with rank r, specifically Õ(r^1.405) per entry update and Õ(r^1.528 + z) per column update, extending to dynamic maximum matching.
Streaming max-cut requires Ω(n) space for dense graphs but Ω(n log(ε² n)/ε²) space for graphs with Θ(n/ε²) edges when outputting the cut, with matching upper bounds for dense case and similar separations for densest subgraph.
The one-way communication complexity of reporting k-edit occurrences (including the edit sequences) is Θ(n/m · k log(m|Σ|/k)) bits for 0 < k < m < n/2.
A cut-preserving sparsifier constructed from approximate max-flow enables faster all-pairs minimum-cut algorithms in unweighted graphs across cut-query, dynamic, and streaming models.
Regularity in hypergraphs is fine-grained equivalent to the general case for clique detection, enabling a complete classification of k-sparse Boolean CSP optimization complexity by constraint degree: linear for d≤1, clique-equivalent for d=2, and exhaustive-search for d≥3 under 3-uniform hyperclique
Small symmetries create strict hierarchies in resolution with exponential separations from standard resolution, constant-depth Frege, and between SRCI and SRII.
Deterministic Õ(n^{ω(σ)}) time algorithm for multi-source reachability in digraphs with n^σ sources, improving prior randomized n^{1+2/3ω(σ)} bound.
cgFOC admits computable VC-dimension bounds on nowhere dense structures and efficient algorithms for query answering and PAC learning on locally bounded expansion classes, but a minor extension is intractable on trees.
Uniform-Ironed-Virtual-Value Item Pricing achieves a tight 3-approximation to the Duality Relaxation Benchmark in unit-demand single-buyer revenue maximization.
Any n-qubit QC Hamiltonian sparsifies to Õ(n/ε²) terms preserving all state energies within 1±ε using invariant subspace decomposition and the Alon-Kozma operator inequality.
The paper shows fine-grained hardness for approximating reachability diameter in directed graphs, gives additive approximations for unweighted cases, and constant-factor approximations for bounded treewidth and width-bounded DAGs.
First learning-augmented algorithms for online minimization problems that use stable dual LP predictions to improve theoretical guarantees on metrical task systems and laminar set cover.
Sparsity helps for k-independent set only below certain density thresholds, with new algorithms achieving O(min(n^{ωk/3} + m^{k/3}, n^k)) time and conditional lower bounds showing brute-force necessity above thresholds for many binary constraint families.
GenusSink delivers near-linear-time approximate generalized Sinkhorn algorithms for bounded-genus graphs via separator decompositions, computational geometry, and fast matrix-vector multiplies with generalized distance matrices.
Rigorous security proofs for variable-length QKD, phase-error bounding with imperfect detectors, marginal-constrained entropy accumulation, and authentication reductions place practical QKD on firmer mathematical ground.
Semialgebraic graphs admit O(n^{1-2/(d+1)+ε})-bit adjacency labels via polynomial partitioning; semilinear graphs need only O(log n) bits.
Connectivity-preserving important separators of size at most k number 2^{O(k log k)} and can be enumerated in the same bound, yielding 2^{O(k log k)} FPT time for constant-class Node Multiway Cut-Uncut.
Incremental (1-ε)-approximate s-t max-flow algorithm achieving Õ(m + n F*/ε) total update time, first with polylog amortized updates for dense graphs.
First practical algorithm for expander hierarchies used to build a normalized-cut solver that beats state-of-the-art quality on large real-world graphs.
Introduces approximation-preserving coresets that guarantee cost preservation for near-optimal solutions and proves that even tiny approximation-factor distortion forbids coresets of that size.
A GNN trained on bipartite alignment graphs between references and LLM generations reports state-of-the-art hallucination detection across four datasets, beating prior methods and GPT-4o.
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Benchmark-Tight Approximation Ratio of Simple Mechanism for a Unit-Demand Buyer
Uniform-Ironed-Virtual-Value Item Pricing achieves a tight 3-approximation to the Duality Relaxation Benchmark in unit-demand single-buyer revenue maximization.