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 54
Protected tails and polynomial-time enumeration of permutations avoiding a direct sum of an increasing pattern and 231
We give an exact algorithm counting the permutations that avoid a fixed pattern from the following family: the direct sum of an increasing pattern and the pattern 231.Breaking the 1/3 Barrier for $\boldsymbol{k}$-Submodular Maximization under Matroid and Knapsack Constraints: A Proportional Top-2 Randomized Framework
$k$-submodularity generalizes submodularity by allowing each selected element to be assigned one of $k$ labels, rather than being merely selected or not selected.Consistency-Robustness Tradeoffs for Online Bipartite Allocation with Multiple Stages
We study learning-augmented online bipartite allocation with multiple stages.On the Hardness of Maximin Share Allocations
The maximin share (MMS) guarantee is a central fairness benchmark for allocating indivisible items.Scalable Triangle Counting: The Threshold Algorithm
We study one-pass triangle counting on random-order edge streams.Thin-shell stability of Gaussian cooling: logconcave sampling with sesteric complexity from a cold start
We show that logconcave probability measures along the Gaussian cooling path have thin-shell stability, generalizing the thin-shell theorem.The $k$-server conjecture is true
The $k$-server conjecture states that a deterministic online algorithm can achieve competitive ratio $k$ on every metric space.A Cheeger Inequality for Hypergraphs and Its Applications
Hypergraphs provide a natural framework for modeling higher-order relationships, but the development of spectral techniques with provable guarantees for general non-uniform hypergraphs remains…SETH-based Lower Bound for Dynamic Degeneracy
In this work, we consider the problem of maintaining an approximate value of degeneracy of a given dynamic $n$-vertex graph $G$ updated by edge insertions and deletions.Low-Degree Polynomial Approximation of the Cross-Polytope
We determine the degree-distortion tradeoff for polynomial approximation of the $d$-dimensional cross-polytope $B_1^d$.A $(p+q)^{O(pq)}$-approximation for $(p, q)$-Flexible Graph Connectivity
In the $(p,q)$-Flexible Graph Connectivity problem, the input consists of non-negative integers $p$ and $q$ and a graph $G=(V, E)$ whose edges are classified into safe and unsafe edges with…Sharp Norms from Finite Structure: Graph Matrices and Structured Chaoses
Graph matrices encode dependencies in random matrices built from shared random variables and arise in spectral algorithms, sum-of-squares (SoS), and high-dimensional statistics.Approximating Optimal Welfare in Complementary Allocation under Decentralized Information
Complementary resources are often allocated by agencies that see different coordinates of an individual's needs.Color Complexity of Recolorable Graph Exploration: Upper and Lower Bounds via Block Structure
We study exploration of anonymous, port-free graphs by a single agent with no internal memory.Private Graph Property Testing
Graph property testing asks whether a massive graph satisfies a given property, or is far from doing so, using only a sublinear number of queries to the graph.Probably correct row echelon form in the F4 algorithm
The computation of row echelon form is one of the main bottlenecks in the F4 algorithm.Toward Optimal Time-Space Tradeoffs for Set Reconciliation
Set reconciliation, where two parties each holding a large set of elements aim to identify their set difference, is a fundamental task in many areas.Degree-Parameterized Analysis of Sampling-Based Online Matching
We study edge-weighted online bipartite matching under random arrival order, parameterized by the maximum offline degree $d$ and sampling fraction $θ$.The Matroid Secretary Conjecture is True
We resolve the matroid secretary conjecture, giving an online algorithm that accepts each element of the offline optimum with probability at least $1/4$.Online matching games in bipartite expanders: applications to bitprobes and dictionaries with non-adaptive probing
A dictionary is a data structure which stores pairs (key, value).