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 31
Deterministic Approximation of the Total Variation Distance Between Spin Systems
We study deterministic relative approximation of the total variation distance between two Gibbs distributions induced by spin systems on the same bounded-degree graph.Local Sensitivity in Exponential Selection: Failure Modes and Valid Calibrations
Selection is a task that chooses one element from a finite public candidate range to maximize a data-dependent score.Faster Planar Graph Algorithms for Connectivity Problems via Meanders
In this paper, we refine the dynamic programming framework based on the sphere cut decomposition designed by Dorn, Penninkx, Bodlaender, and Fomin (ESA 2005) to obtain faster subexponential…Faster Directed Hopsets, Distance Preservers, and Deterministic Shortcut Sets
While there have been many recent advances in getting better tradeoffs for directed distance structures such as hopsets, shortcut sets and distance preservers, most known algorithms are inefficient.Escaping Degeneracy by Following Shadow Edges
The Simplex method is among the most widely used approaches for solving linear programs.Improved Approximations for Vehicle Routing with Nonuniform Speeds
We study vehicle routing with vehicles of different speeds on a complete undirected graph whose vertex set consists of a depot and a set of clients, where the distances satisfy the triangle…A Computationally-Efficient Closed-Form $C^{s,1}$-Extension Formula
We identify explicit closed-form and variational formulae for interpolating the exact values and derivatives through order $s$ of a $C^{s,1}$ function $f:\mathbb{R}^d\to\mathbb{R}$ at $N$ distinct…The Geometry of Hierarchical Navigation: Accuracy and Query Cost for Point Process Input
Large-scale information retrieval systems, including retrieval-augmented generation (RAG) and recommendation engines, widely use multi-layered hierarchical data structures for ultra-fast approximate…Parallel Edge Ranking of Trees
In this work, we prove that computing the edge ranking of a tree in parallel is P-Complete.Coupling Independence Implies Zero-Freeness
For $Δ\ge2$ and $q\ge11Δ/6$, we prove that the antiferromagnetic $q$-state Potts partition function on finite simple graphs of maximum degree at most $Δ$ has no Fisher zeros in a graph-uniform…A Catalytic Algorithm for Transposing Unknown Qutrit Unitaries with Tight Query Bounds
We construct exact deterministic circuits for transposing and inverting an unknown qutrit unitary $U\in\mathrm{SU}(3)$ using only forward queries.Generating cyclic pivot Gray codes for well-ordered $k$-degenerate graphs in constant amortized time
A graph $G$ is $k$-degenerate if there exists an ordering $v_1, v_2, \dots, v_n$ of its vertices such that each vertex $v_i$ has at most $k$ neighbors $v_j$ in $G$ with $j < i$.Envy-free Allocations with Individual Payments
When an envy-free allocation of indivisible goods does not exist, monetary transfers can restore envy-freeness.Almost Optimal Constant-Round Approximation of Dominating Set in Graph Classes with Excluded Minors
For every fixed proper minor-closed class $\mathscr C$ and every $ε>0$, we give a deterministic LOCAL algorithm that returns a dominating set of size at most $(2a(\mathscr C)+1+ε)γ_f(G)$ on every…Packing Diverse Shortest Cycles
Bentert, Fomin, Golovach, Korhonen, Lochet, Panolan, Ramanujan, Saurabh, and Simonov (SODA 2025) initiated the parameterized study of Edge-Disjoint Shortest Cycle Packing: given a weighted graph $G$…Simulated annealing and Weak Poincaré inequalities with inverse-polynomial accuracy for the Sherrington-Kirkpatrick model
We study sampling from the Gibbs distribution of the Sherrington-Kirkpatrick (SK) model with Glauber dynamics.An $n^{0.3+\varepsilon}$-Approximation for Steiner $k$-Forest
We give an $n^{0.3+\varepsilon}$-approximation algorithm for the Steiner $k$-Forest problem, for any constant $\varepsilon>0$.A deterministic algorithm for signing bipartite graphs at the Ramanujan bound
We give a deterministic polynomial-time algorithm for the Bilu--Linial signing problem on bipartite graphs.Breaking the $\sqrt{3}$ Barrier for Maximum Weighted $3$-Set Packing
We give a deterministic polynomial-time $1.6908$-approximation for Maximum Weighted $3$-Set Packing, breaking the $\sqrt3$ locality-gap barrier of squared-weight local search.BetweenCut: Private Heavy-Node Classification with Doubly Logarithmic Error in Tree Height
Finding heavy nodes in a tree---those whose counts exceed a given threshold---is a building block for analysis and learning over structured data.