Theory & Algorithms · Computer Science & AI
Data Structures & Algorithms
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1,174 papers, from 4 September 2026 to 5 November 2026: 1,174 arXiv preprints.
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Newest papers, page 56
Free-Probabilistic State Evolution and Random Matrix Discrepancy
Let $A_1,\ldots,A_n$ be independent $d \times d$ real symmetric Gaussian random matrices, and consider the linear operator $A(x) = n^{-1/2}\sum_{i=1}^n x_i A_i$, $x\in \mathbb{R}^n$.Fast Odd-Permutation Sums in Characteristic Two and Shortest Even Directed Cycles
For a matrix $A$ over a field of characteristic two, let $Φ(A)$ be the sum of its permutation monomials indexed by odd permutations.Accelerating the Local Push Primitive for PageRank Computation
We propose a local algorithm that computes an $\varepsilon$-approximate PageRank vector in the sense of Andersen, Chung, and Lang (ACL; Internet Math.A Non-constant Lower Bound for Grammar-Based Compression with Greedy
We prove a lower bound of Ω(log n/ log log n) on the approximation ratio of the global grammar-based compression algorithm Greedy.Motifs in temporal hypergraphs
Network motifs, recurrent local patterns of interactions in graphs, provide fundamental insights on the interplay between structure and functionality in complex systems.A Tight $\widetilde Ω(\sqrt{m})$ Information-Theoretic Lower Bound for Randomized Online Set Cover
Online set cover is a fundamental problem in online algorithms, admitting a deterministic $O(\log m\log n)$-competitive algorithm, where $m$ is the number of sets and $n$ is the number of elements.Exponential Lower Bounds for Integer-Weighted Shortest-Paths Preservers of DAGs
We study a graph simplification problem introduced by Bernstein, Bodwin, and Wein [ITCS'24].Learning Sparse Quantum States
We study the problem of tomography for $k$-sparse quantum states.Streaming Algorithms for Gaussian Kernel Density Statistics
Motivated by data produced by generative systems, \cite{LZ26b} formulates similarity-aware statistics via a weighted similarity graph, replacing equality with similarity in classical frequency-based…Scalable Composition of Byzantine Agreements under Reorder Attacks
Byzantine agreement (BA) is a foundational building block in distributed systems, and the security analysis of BA protocols under multi-instance executions has attracted increasing attention.Fast Algorithms for Sparse PCA and Robust Sparse Estimation
We study fast algorithms for sparse-PCA certification.Online Inverse Integer Linear Optimization via Small-Gradient Skipping: Constant Regret and Finite Mistakes
In online inverse linear optimization, the learner predicts a weight at each round, observes the optimal action of the agent, and updates its prediction.On the Parameterized Complexity of Coloring Discovery
Coloring Discovery asks whether a possibly improper initial coloring can be made proper within a prescribed number of allowed changes.A Sharp Barrier for Consistent Submodular Maximization: Any Improvement over $2-\sqrt{2}$ Entails Exponential Queries or Linear Recourse
Consistent submodular maximization studies the tradeoff between solution quality and stability when elements arrive over time.Minimum-makespan completion and vertex selection leave the Wang-Sitters constant at 11/6
The 11/6 worst-case constant of the Wang-Sitters rounding scheme, which a companion note establishes, can naturally be attributed to the freedom in Step 3, where an arbitrary valid slot matching is…Introvert Clustering for Distributed Graph Algorithms
We introduce a graph decomposition primitive called introvert clustering, which strengthens standard low-diameter clustering by guaranteeing that every clustered vertex keeps at least a…Optimal Non-Adaptive Vantage Point Selection
We study the \emph{vantage point selection} problem, introduced by Ashvinkumar, Chowdhury, Gao, Goswami, Mitchell, and Polishchuk [WADS'25] to model the problem of estimating bottleneck capacities…Testing the Binary Rank with Polynomial Query Complexity
We provide an adaptive two-sided error testing algorithm for the binary rank of a $0,1$ matrix $M$ with query complexity $O(d^3\log(d+1)/ε^2)$, where $d$ is the tested binary rank bound and $ε$ is…Optimal Low-Rank Quantum State Tomography with Bounded-Sample Joint Measurements
We determine the optimal sample complexity of low-rank quantum state tomography when each measurement may act jointly on at most $t$ samples.Subexponential Approximation of the Permanent in Deterministic Polynomial Time
We give the first deterministic polynomial time algorithm that approximates the permanent of arbitrary nonnegative rational matrices within a subexponential factor.