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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2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS) , pages =
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Randomized LOCAL algorithm computes 2-ruling sets in O(log log n) rounds w.h.p. on graphs with arboricity O(log log n), nearly matching lower bounds and exponentially improving prior combinations of results.
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.
The work proves that approximating correlation clustering to additive εn² error requires Ω(n/ε²) adjacency-matrix queries, with stronger bounds under memory constraints in random and general query models.
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.
An algorithm for online Steiner forest achieves constant competitiveness with amortized O(log n) recourse.
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.
Tight single-pass linear-space lower bounds for approximating arbitrary Max-CSP(F) whenever the basic LP admits a (γ,β)-integrality gap.
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.
Counting induced k-vertex subgraphs with automorphism group exactly Q is #W[1]-hard for every finite group Q, via clique-scaffold reductions from k-clique.
Improved (O(pw), Δ)-LDD for pathwidth-pw digraphs and O(tw log n) integrality gap for directed sparsest-cut LP on treewidth-tw graphs via refined quasipartition analysis.
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.
Introduces forward-assisted purification via a new spatiotemporal framework that outperforms conventional static purification by up to 50x in copy efficiency and circumvents no-purification theorems for Bell states.
Introduces a distributed stochastic setting for graph optimization and supplies fast approximation algorithms for matching, vertex cover, and dominating set that surpass non-stochastic lower bounds.
The quantum homomorphism quasi-order of finite directed graphs and of finite planar graphs with maximum degree at most 7 is countably universal.
Hybrid sketching saves up to 97% space on dense graphs and 15% on sparse ones by sketching dense cores and storing sparse parts exactly, with new BalloonSketch reducing sketch sizes up to 8x.
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.
Three new robust error models for catalytic tape resetting are characterized with equivalences to standard classes and collapse under derandomization.
A two-pass sublinear-space streaming algorithm achieves (1/2-ε)-approximation for Max-DICUT on unbounded-degree graphs.
First efficient sum-of-squares algorithms recover exact and approximate overlapping planted cliques in dense random intersection graphs for k ≫ √(n log n), with robustness to noise, monotone adversaries, and optimal edge corruptions.
Generalizes homomorphism indistinguishability equivalences induced by orthogonal easy quantum groups, including a classification of (0,0)-intertwiners for graph-theoretic versions.
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.
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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.