This paper proposes two algorithms for approximating the number of four-cycles in graph edge streams, improving upon existing theoretical bounds and handling non-concentrated four-cycles in one-pass.

This paper identifies a tractability island inside the contextual-fraction problem by collapsing it to a fixed-point calculation for a specific class of permutation-transport models.

The paper provides a tight, transparent, and closed-form analysis of the trade-off function for Differentially Private SGD using random shuffling, significantly improving upon previous methods and est…

The polynomial-time low-degree conjecture, which predicts that low-degree indistinguishability, a uniform null distribution, permutation invariance, and independent resampling imply polynomial-time ha…

The paper uses majorization theory to analyze lattice reduction, showing that local swaps smooth the Gram-Schmidt profile and deriving variational and telescoping identities for the worst-case profile…

A new solver-free parallel spectral sparsification algorithm for weighted graphs is presented, relying on low-diameter decompositions and independent sampling, eliminating dependence on target approxi…

The paper proves an information-theoretically optimal gap-majority lemma in the two-player randomized communication model, achieving the correct linear scaling and constant-constant tradeoff.

This paper introduces Electric Flow Sampling (elfs) as a zero-error quantum walk primitive and uses it to derive improved quantum algorithms for various graph problems, including semi-supervised learn…

Chen et al. prove a Poincaré inequality for Glauber dynamics of hard-core model on random regular graphs using Bochner--Bakry--Émery approach.

The paper analyzes low-degree estimation thresholds for recovering hidden signals in planted hypergraphs and tensor PCA, establishing sharp phase transitions and providing polynomial-time recovery alg…

This paper presents a local computation algorithm to approximate the top eigenvector of a symmetric matrix with entries between -1 and 1, building on Swartworth and Woodruff's work.

This paper presents a polynomial-time differentially private algorithm for releasing a synthetic graph that approximates cut sizes in an input graph with error bound.

This paper studies the triangle-densest-$k$-subgraph problem in an average-case model and proposes spectral and semidefinite algorithms for its recovery.

The paper proves a stochastic comparison for Gaussian maxima, resolving the Weak Simplex Conjecture and proving the Simplex Mean Width Conjecture.

This paper provides bounds on the difference between the annihilation number and independence number of a finite simple graph, and proves these bounds for various types of graphs.

This paper proves space lower bounds for entropy-efficient random sampling using i.i.d. uniform bits.

This paper presents conditions for achieving optimal uniformity in Quasi-Monte Carlo estimators using Sobol' sequences and Artin-Schreier polynomials.