Tootfinder

Solving Convex-Concave Problems with $\tilde{\mathcal{O}}(\epsilon^{-4/7})$ Second-Order Oracle Complexity
Lesi Chen, Chengchang Liu, Luo Luo, Jingzhao Zhang
https://arxiv.org/abs/2506.08362

Solving Convex-Concave Problems with $\tilde{\mathcal{O}}(ε^{-4/7})$ Second-Order Oracle Complexity
Previous algorithms can solve convex-concave minimax problems $\min_{x \in \mathcal{X}} \max_{y \in \mathcal{Y}} f(x,y)$ with $\mathcal{O}(ε^{-2/3})$ second-order oracle calls using Newton-type methods. This result has been speculated to be optimal because the upper bound is achieved by a natural generalization of the optimal first-order method. In this work, we show an improved upper bound of $\tilde{\mathcal{O}}(ε^{-4/7})$ by generalizing the optimal second-order method for convex optimizat…

This https://arxiv.org/abs/2502.07995 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Genuine multi-entropy and holography
Is bipartite entanglement sufficient for holography? Through the analysis of the Markov gap, it is known that the answer is no. In this paper, we give a new perspective on this issue from a different angle using a multi-entropy. We define a genuine $\mathtt{q}$-partite multi-entropy from a $\mathtt{q}$-partite multi-entropy by subtracting appropriate linear combinations of $\mathtt{\tilde{q}}$-partite multi-entropies for $\mathtt{\tilde{q}} < \mathtt{q}$, in such a way that the genuine $\mathtt…

Solving fuzzy linear systems in Gaussian PDMF space
Chuang Zheng
https://arxiv.org/abs/2508.04709 https://arxiv.org/pdf/2508.04709

Solving fuzzy linear systems in Gaussian PDMF space
In the first part of the paper, we solve the semi-fuzzy linear system (SFLS) $A \mathbf{\tilde{x}}= \mathbf{\tilde{b}}$, where $A\in \mathbb{R}^{m\times n}$ is a real-valued matrix, $\mathbf{\tilde{b}}$ is a fuzzy number vector, and $\mathbf{\tilde{x}}$ is the unknown fuzzy number vector. The elements of both $\mathbf{\tilde{b}}$ and $\mathbf{\tilde{x}}$ belong to a fuzzy number space $\mathcal{X}$, namely the Gaussian probability density membership function (Gaussian-PDMF) space. We present th…

Constraints on Symmetric Dark Matter from Neutron Star Capture and Collapse
Yuxin Liu, Zhen Liu, Maxim Pospelov, Sanjay Reddy
https://arxiv.org/abs/2508.04961 https://

Constraints on Symmetric Dark Matter from Neutron Star Capture and Collapse
Dark matter (DM) models with a conserved particle$-$antiparticle number, $n_χ-n_{\tilde χ}$, and the asymmetry in the cosmological abundance $n_χ\neq n_{\tilde χ}$, are known to be challenged by the existence of old neutron stars (NSs), as the sufficient accumulation of DM will lead to the collapse of NSs into black holes. We demonstrate that the applicability of these constraints is much wider and covers models with symmetric populations of DM, $n_χ= n_{\tilde χ}$, as the process of DM c…

Parallel Batch-Dynamic Coreness Decomposition with Worst-Case Guarantees
Mohsen Ghaffari, Jaehyun Koo
https://arxiv.org/abs/2507.06334 https://

Parallel Batch-Dynamic Coreness Decomposition with Worst-Case Guarantees
We present the first parallel batch-dynamic algorithm for approximating coreness decomposition with worst-case update times. Given any batch of edge insertions and deletions, our algorithm processes all these updates in $ \text{poly}(\log n)$ depth, using a worst-case work bound of $b\cdot \text{poly}(\log n)$ where $b$ denotes the batch size. This means the batch gets processed in $\tilde{O}(b/p)$ time, given $p$ processors, which is optimal up to logarithmic factors. Previously, an algorithm …

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Unitary designs in nearly optimal depth
Laura Cui, Thomas Schuster, Fernando Brandao, Hsin-Yuan Huang
https://arxiv.org/abs/2507.06216 https://

Unitary designs in nearly optimal depth
We construct $\varepsilon$-approximate unitary $k$-designs on $n$ qubits in circuit depth $O(\log k \log \log n k / \varepsilon)$. The depth is exponentially improved over all known results in all three parameters $n$, $k$, $\varepsilon$. We further show that each dependence is optimal up to exponentially smaller factors. Our construction uses $\tilde{O}(nk)$ ancilla qubits and ${O}(nk)$ bits of randomness, which are also optimal up to $\log(n k)$ factors. An alternative construction achieves a…

Parallel Batch-Dynamic Algorithms for Spanners, and Extensions
Mohsen Ghaffari, Jaehyun Koo
https://arxiv.org/abs/2507.06338 https://…

Parallel Batch-Dynamic Algorithms for Spanners, and Extensions
This paper presents the first parallel batch-dynamic algorithms for computing spanners and sparsifiers. Our algorithms process any batch of edge insertions and deletions in an $n$-node undirected graph, in $\text{poly}(\log n)$ depth and using amortized work near-linear in the batch size. Our concrete results are as follows: - Our base algorithm maintains a spanner with $(2k-1)$ stretch and $\tilde{O}(n^{1+1/k})$ edges, for any $k\geq 1$. - Our first extension maintains a sparse spanner wit…

Intertwining Algebras and Affine Hecke Algebras for Finite Central Extensions of Classical $p$-adic Groups with Application to Metaplectic Groups
Volker Heiermann, Chenyan Wu
https://arxiv.org/abs/2508.04303

Intertwining Algebras and Affine Hecke Algebras for Finite Central Extensions of Classical $p$-adic Groups with Application to Metaplectic Groups
For a finite central extension $\tilde{G}$ of a classical $p$-adic reductive group, we consider the endomorphism algebra of some induced projective generator à la Bernstein of the category of smooth representations of $\tilde{G}$. In the case where the Levi subgroups decompose, we can compute this algebra to get a result similar to the one previously obtained by the first author for classical $p$-adic groups, showing that this intertwining algebra is a twisted semi-direct product of an affine …

Faster Distributed $\Delta$-Coloring via a Reduction to MIS
Yann Bourreau, Sebastian Brandt, Alexandre Nolin
https://arxiv.org/abs/2508.01762 https://arxiv…

Faster Distributed $Δ$-Coloring via a Reduction to MIS
Recent improvements on the deterministic complexities of fundamental graph problems in the LOCAL model of distributed computing have yielded state-of-the-art upper bounds of $\tilde{O}(\log^{5/3} n)$ rounds for maximal independent set (MIS) and $(Δ+ 1)$-coloring [Ghaffari, Grunau, FOCS'24] and $\tilde{O}(\log^{19/9} n)$ rounds for the more restrictive $Δ$-coloring problem [Ghaffari, Kuhn, FOCS'21; Ghaffari, Grunau, FOCS'24; Bourreau, Brandt, Nolin, STOC'25]. In our work, we show that $Δ$-col…

Diffeomorphic approximation of piecewise affine homeomorphisms
Daniel Campbell, Luigi D'Onofrio, Tom\'a\v{s} V\'itek
https://arxiv.org/abs/2507.02854

Diffeomorphic approximation of piecewise affine homeomorphisms
Given any $f$ a locally finitely piecewise affine homeomorphism of $Ω\subset \mathbb{R}^d$ onto $Δ\subset \mathbb{R}^d$ (for $d=3, 4$) such that $f\in W^{1,p}(Ω, \mathbb{R}^d)$ and $f^{-1}\in W^{1,q}(Δ, \mathbb{R}^d)$, $1\leq p ,q < \infty$ and any $ε>0$ we construct a diffeomorphism $\tilde{f}$ such that $$\|f-\tilde{f}\|_{W^{1,p}(Ω,\mathbb{R}^d)} + \|f^{-1}-\tilde{f}^{-1}\|_{W^{1,q}(Δ,\mathbb{R}^d)} < ε.$$

This https://arxiv.org/abs/1911.02653 has been replaced.
link: https://scholar.google.com/scholar?q=a

Analysis of Two-variable Recurrence Relations with Application to Parameterized Approximations
In this paper we introduce randomized branching as a tool for parameterized approximation and develop the mathematical machinery for its analysis. Our algorithms improve the best known running times of parameterized approximation algorithms for Vertex Cover and $3$-Hitting Set for a wide range of approximation ratios. One notable example is a simple parameterized random $1.5$-approximation algorithm for Vertex Cover, whose running time of $\tilde{O}(1.01657^k)$ substantially improves the best k…

I just found out by trying, that on my Linux install
Alt Gr - = – (why would anyone use em dashes? those are way too long anyway. en dashes is where it's at.)
Alt Gr . = … (OMG, yes! Windows with its Alt 0,1,3,3 can go suck it!)
Alt Gr , = · (… tf is a middledot?)
Thanks for the inspiration, Wolfgang!
htt…

Why So Many Women Are Quitting the Workforce | TIME http://about:reader?url=https://time.com/7306896/women-leaving-workforce/?utm_source=firefox-newtab-en-us

This https://arxiv.org/abs/2504.18292 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Large time cumulants of the KPZ equation on an interval
We consider the Kardar-Parisi-Zhang equation on the interval $[0,L]$ with Neumann type boundary conditions and boundary parameters $u,v$. We show that the $k$-th order cumulant of the height behaves as $c_k(L,u,v)\, t$ in the large time limit $t \to +\infty$, and we compute the coefficients $c_k(L,u,v)$. We obtain an expression for the upper tail large deviation function of the height. We also consider the limit of large $L$, with $u=\tilde u/\sqrt{L}$, $u=\tilde v/\sqrt{L}$, which should give …

The monomial expansions for modified Macdonald polynomials
Emma Yu Jin, Xiaowei Lin
https://arxiv.org/abs/2506.23373 https://arxiv.or…

The monomial expansions for modified Macdonald polynomials
We discover a family $A$ of sixteen statistics on fillings of any given Young diagram and prove new combinatorial formulas for the modified Macdonald polynomials, that is, $$\tilde{H}_λ(X;q,t)=\sum_{σ\in T(λ)}x^σq^{maj(σ)}t^{η(σ)}$$ for each statistic $η\in A$. Building upon this new formula, we establish four compact formulas for the modified Macdonald polynomials, namely, $$\tilde{H}_λ(X;q,t)=\sum_σd_{\varepsilon}(σ)x^σq^{maj(σ)}t^{η(σ)}$$ which is summed over all canonical or …

Green\'s Mapping and Julia Sets
Ilia Binder, Paul F. X. M\"uller, Peter Yuditskii
https://arxiv.org/abs/2508.04207 https://arxiv.org/pdf/2508.0420…

Greenś Mapping and Julia Sets
In March 1999, the first named author (Binder) posed the problem of showing that a ``good direction'' $ψ\in [0,2]$ exists, for any Green's mapping $T:H\rightarrow\tilde Ω$, i.e., \begin{equation}\label{binder} \int\limits_0\limits^{1} |T''(re^{iπψ})|dr <\infty, \quad\text{ for at least one } \quad ψ\in [0,2]. \end{equation} Presently this problem is open even in the special case where $\partial Ω$ is a uniformly perfect subset of the real line. In this paper we obtain a posi…

Faster negative length shortest paths by bootstrapping hop reducers
Yufan Huang, Peter Jin, Kent Quanrud
https://arxiv.org/abs/2506.00428 https://

Faster negative length shortest paths by bootstrapping hop reducers
The textbook algorithm for real-weighted single-source shortest paths takes $O(m n)$ time on a graph with $m$ edges and $n$ vertices. The breakthrough algorithm by Fineman [Fin24] takes $\tilde{O}(m n^{8/9})$ randomized time. The running time was subsequently improved to $\tilde{O}(mn^{4/5})$ [HJQ25]. We build on [Fin24; HJQ25] to obtain an $\tilde{O}(m n^{3/4} + m^{4/5} n)$ randomized running time. (Equivalently, $\tilde{O}(mn^{3/4})$ for $m \geq n^{5/4}$, and $\tilde{O}(m^{4/5} n)$ for $m \…

Non-isomorphic subfields of the BM and GGS maximal function fields
Peter Beelen, Tobias Drue, Maria Montanucci, Giovanni Zini
https://arxiv.org/abs/2506.20210

Non-isomorphic subfields of the BM and GGS maximal function fields
In 2016 Tafazolian et al. introduced new families of $\mathbb{F}_{q^{2n}}$-maximal function fields $\mathcal{Y}_{n,s}$ and $\mathcal{X}_{n,s,a,b}$ arising as subfields of the first generalized GK function field (GGS). In this way the authors found new examples of maximal function fields that are not isomorphic to subfields of the Hermitian function field. In this paper we construct analogous function fields $\tilde{\mathcal{Y}}_{n,s}$ and $\tilde{\mathcal{X}}_{n,s,a,b}$ as subfields of the seco…

Replaced article(s) found for cs.LG. https://arxiv.org/list/cs.LG/new
[2/5]:
- An $\tilde{O}$ptimal Differentially Private Learner for Concept Classes with VC Dimension 1
Chao Yan

Spin Seebeck Effect of Triangular-lattice Spin Supersolid
Yuan Gao, Yixuan Huang, Sadamichi Maekawa, Wei Li
https://arxiv.org/abs/2506.22414 https://

Spin Seebeck Effect of Triangular-lattice Spin Supersolid
Using our developed thermal tensor-network approach, we investigate the spin Seebeck effect (SSE) of the triangular-lattice quantum antiferromagnet hosting spin supersolid phase. We focus on the low-temperature scaling of normalized spin current $\tilde{I}_S$ through the interface, and benchmark our approach on 1D Heisenberg chain, with the negative spinon spin current reproduced. In addition, we find an algebraic scaling $\tilde{I}_S \sim T^α$ with varying exponent $α$ in the Tomonaga-Luttin…

Twisted associative algebras associated to vertex algebras
Shun Xu
https://arxiv.org/abs/2506.01321 https://arxiv.org/pdf/2506.01321

Twisted associative algebras associated to vertex algebras
Let $V$ be a vertex algebra and $g$ an automorphism of $V$ of order $T$. We construct a sequence of associative algebras $\tilde{A}_{g,n}(V )$ for any $n\in(1/T)\mathbb{N}$, which are not depend on the conformal structure of $V$. We show that for a vertex operator algebra, $g$-rationality, $g$-regularity, and twisted fusion rules are independent of the choice of the conformal vector.

This https://arxiv.org/abs/2504.15816 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Toward optimal-scaling DFT: stochastic Hartree theory in the thermodynamic and complete basis set limits at arbitrary temperature
We present the first mathematical analysis of stochastic density functional theory (DFT) in the context of the Hartree approximation. We motivate our analysis via the notion of nearly-optimal or $\tilde{O}(n)$ scaling with respect to the number $n$ of computational degrees of freedom, independent of the number of electrons, in both the thermodynamic and complete basis set limits. Indeed, the promise of such scaling is the primary motivation for stochastic DFT relative to conventional orbital-ba…

This https://arxiv.org/abs/2504.05655 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multi-bubble solutions for the Dirichlet problem of the $H$-system with higher degree
We consider a Dirichlet problem of the $H$-system \begin{equation*} \begin{cases} Δv = 2v_x\wedge v_y ~& \text{ in }\mathcal{D},\\ v=\varepsilon \tilde g ~& \text{ on }\partial{\mathcal{D}}, \end{cases} \end{equation*} where $\mathcal D\subset \mathbb{R}^2$ is the unit disk, $v:\mathcal D\to \mathbb{R}^3$, and $\tilde g:\partial \mathcal D\to \mathbb{R}^3$ is a given smooth map. As $\varepsilon\to 0^+$, we construct multi-bubble solutions concentrating at distinct points, taking around each po…

White House pressure for increased immigration arrests strains law enforcement agencies | CNN Politics
https://edition.cnn.com/2025/05/29/politics/white-house-immigration-arrests-law-enforcement-agencies
America is less secured now. Officers are stopping care of real issues.

Trinitary algebras
V. A. Vassiliev
https://arxiv.org/abs/2506.12865 https://arxiv.org/pdf/2506.12865…

Trinitary algebras
A {\em trinitary algebra} is any subalgebra of the space of smooth functions $f: M \to {\mathbb R}$ that is distinguished in this space by finitely many linear conditions of the form $f(x_i) = f(\tilde x_i) = f(\hat x_i)$, where $x_i, \tilde x_i,$ and $ \hat x_i $ are distinct points in $ M$, $i=1, \dots, k$, or is approximated by such subalgebras. These algebras naturally arise in the study of discriminant varieties, i.e., the spaces of singular geometric objects, in theories where the propert…

Eigenfunction asymptotics in the complex domain for a compact Lie group
Simone Gallivanone, Roberto Paoletti
https://arxiv.org/abs/2507.18285 https://arxiv…

Eigenfunction asymptotics in the complex domain for a compact Lie group
Let $(G,κ)$ be a compact connected Lie group endowed with a biinvariant Riemannian metric, and let $\tilde{G}$ be the complexification of $G$. We apply Grauert tube techniques to the near-diagonal scaling asymptotics of certain operator kernels, which are defined in terms of the matrix elements of an irreducuble representation drifting to infinity along a ray in weight space. These kernels are the equivariant components of Poisson and Szegő kernels on a fixed sphere bundle in $\tilde{G}$, whe…

This https://arxiv.org/abs/2111.14528 has been replaced.
link: https://scholar.google.com/scholar?q=a

Reconstruction and interpolation of manifolds II: Inverse problems with partial data for distances observations and for the heat kernel
We consider how a closed Riemannian manifold $M$ and its metric tensor $g$ can be approximately reconstructed from local distance measurements. Moreover, we consider an inverse problem of determining $(M,g)$ from limited knowledge on the heat kernel. In the part 1 of the paper, we considered the approximate construction of a smooth manifold in the case when one is given the noisy distances $\tilde d(x,y)=d(x,y)+\varepsilon_{x,y}$ for all points $x,y\in X$, where $X$ is a $δ$-dense subset of $M…

Faster MPC Algorithms for Approximate Allocation in Uniformly Sparse Graphs
Jakub {\L}\k{a}cki, Slobodan Mitrovi\'c, Srikkanth Ramachandran, Wen-Horng Sheu
https://arxiv.org/abs/2506.04524

Faster MPC Algorithms for Approximate Allocation in Uniformly Sparse Graphs
We study the allocation problem in the Massively Parallel Computation (MPC) model. This problem is a special case of $b$-matching, in which the input is a bipartite graph with capacities greater than $1$ in only one part of the bipartition. We give a $(1+ε)$ approximate algorithm for the problem, which runs in $\tilde{O}(\sqrt{\log λ})$ MPC rounds, using sublinear space per machine and $\tilde{O}(λn)$ total space, where $λ$ is the arboricity of the input graph. Our result is obtained by pro…

Markov dualities via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right and left eigenvectors
Cecile Monthus
https://arxiv.org/abs/2507.11041

Markov dualities via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right and left eigenvectors
The notion of Markov duality between two Markov processes that can live in two different configurations spaces $(x,{\tilde x})$ is revisited via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right and left eigenvectors. In this formulation, the two generators should have the same eigenvalues $(-E)$ that may be complex, while the duality function $Ω(x,{\tilde x})$ can be considered as a mapping between the right and the left eigenvectors of the two mod…

Rapid Mixing of Glauber Dynamics for Monotone Systems via Entropic Independence
Weiming Feng, Minji Yang
https://arxiv.org/abs/2507.11031 https://

Rapid Mixing of Glauber Dynamics for Monotone Systems via Entropic Independence
We study the mixing time of Glauber dynamics on monotone systems. For monotone systems satisfying the entropic independence condition, we prove a new mixing time comparison result for Glauber dynamics. For concrete applications, we obtain $\tilde{O}(n)$ mixing time for the random cluster model induced by the ferromagnetic Ising model with consistently biased external fields, and $\tilde{O}(n^2)$ mixing time for the bipartite hardcore model under the one-sided uniqueness condition, where $n$ is …

Zeros of linear combinations of Laguerre polynomials
Antonio J. Dur\'an
https://arxiv.org/abs/2507.22425 https://arxiv.org/pdf/2507.22425

Zeros of linear combinations of Laguerre polynomials
We study the number of real zeros of finite combinations of $K+1$ consecutive normalized Laguerre polynomials of the form $$ q_n(x)=\sum_{j=0}^Kγ_j\tilde L^α_{n-j}(x),\quad n\ge K, $$ where $γ_j$, $j=0,\cdots ,K$, are real numbers with $γ_0=1$, $γ_K\not =0$. We consider four different normalizations of Laguerre polynomials: the monic Laguerre polynomials $\hat L_n^α$, the polynomials $\mathcal L_n^α=n!L_n^α/(1+α)_n$ (so that $\mathcal L_n^α(0)=1$), the standard Laguerre polynomials $(…

Introducing Marginalian Editions: Extraordinary Forgotten Books Brought Back to Life – The Marginalian
https://www.themarginalian.org/2025/04/24/introducing-marginalian-editions/

This https://arxiv.org/abs/2306.14853 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Near-Optimal Nonconvex-Strongly-Convex Bilevel Optimization with Fully First-Order Oracles
In this work, we consider bilevel optimization when the lower-level problem is strongly convex. Recent works show that with a Hessian-vector product (HVP) oracle, one can provably find an $ε$-stationary point within ${\mathcal{O}}(ε^{-2})$ oracle calls. However, the HVP oracle may be inaccessible or expensive in practice. Kwon et al. (ICML 2023) addressed this issue by proposing a first-order method that can achieve the same goal at a slower rate of $\tilde{\mathcal{O}}(ε^{-3})$. In this pap…

Improved Algorithms for Effective Resistance Computation on Graphs
Yichun Yang, Rong-Hua Li, Meihao Liao, Guoren Wang
https://arxiv.org/abs/2507.04674 http…

Improved Algorithms for Effective Resistance Computation on Graphs
Effective Resistance (ER) is a fundamental tool in various graph learning tasks. In this paper, we address the problem of efficiently approximating ER on a graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$ with $n$ vertices and $m$ edges. First, we focus on local online-computation algorithms for ER approximation, aiming to improve the dependency on the approximation error parameter $ε$. Specifically, for a given vertex pair $(s,t)$, we propose a local algorithm with a time complexity of $\tilde{O…

Experimental Design for Semiparametric Bandits
Seok-Jin Kim, Gi-Soo Kim, Min-hwan Oh
https://arxiv.org/abs/2506.13390 https://arxiv.o…

Experimental Design for Semiparametric Bandits
We study finite-armed semiparametric bandits, where each arm's reward combines a linear component with an unknown, potentially adversarial shift. This model strictly generalizes classical linear bandits and reflects complexities common in practice. We propose the first experimental-design approach that simultaneously offers a sharp regret bound, a PAC bound, and a best-arm identification guarantee. Our method attains the minimax regret $\tilde{O}(\sqrt{dT})$, matching the known lower bound for …

$H^s_x$ regularity of solutions to the stationary Boltzmann equation with the incoming boundary condition
Daisuke Kawagoe
https://arxiv.org/abs/2507.18211 https://

$H^s_x$ regularity of solutions to the stationary Boltzmann equation with the incoming boundary condition
We consider the stationary Boltzmann equation with the cross section of the form $B(|v - \tilde{v}, θ|) = B_0 |v - \tilde{v}|^γ\cos θ\sin θ$ for $-3 < γ\leq 1$ in a bounded convex domain under the incoming boundary condition. In this article, we shall show the existence of a solution in a weighted $L^\infty$ space with fractional Sobolev regularity without assuming the positivity of the Gaussian curvature on the boundary. For boundary data sufficiently smooth and close …

Canonical Partition Function on a Quantum Computer through Trotter Interpolation
Taozhi Guo, Gumaro Rendon, Rutuja Kshirsagar
https://arxiv.org/abs/2506.09318

Canonical Partition Function on a Quantum Computer through Trotter Interpolation
In this work, we present a Gibbs state observable estimation algorithm based on Trotter interpolation, which reaches a state-of-the-art quantum computational cost of $ \tilde{O}(β\log{1/ε})$. Our approach saves $\log(Γ)$ ancilla qubits compared with the qubitization-based methods for Hamiltonian with $Γ$ stages. To provide a robust assessment of our approach, we benchmark our results against state-of-the-art methodology using the SYK model as a testbed. Our method provides an efficient alte…

Improved 2-Approximate Shortest Paths for close vertex pairs
Manoj Gupta
https://arxiv.org/abs/2507.19859 https://arxiv.org/pdf/2507.19859

Improved 2-Approximate Shortest Paths for close vertex pairs
An influential result by Dor, Halperin, and Zwick (FOCS 1996, SICOMP 2000) implies an algorithm that can compute approximate shortest paths for all vertex pairs in $\tilde{O}(n^{2+O\left(\frac{1}{k}\right )})$ time, ensuring that the output distance is at most twice the actual shortest path, provided the pairs are at least $k$ apart, where $k \ge 2$. We present the first improvement on this result in over 25 years. Our algorithm achieves roughly same $\tilde{O}(n^{2+\frac{1}{k}})$ runtime but a…

New algorithms for girth and cycle detection
Liam Roditty, Plia Trabelsi
https://arxiv.org/abs/2507.02061 https://arxiv.org/pdf/2507.…

New algorithms for girth and cycle detection
Let $G=(V,E)$ be an unweighted undirected graph with $n$ vertices and $m$ edges. Let $g$ be the girth of $G$, that is, the length of a shortest cycle in $G$. We present a randomized algorithm with a running time of $\tilde{O}\big(\ell \cdot n^{1 + \frac{1}{\ell - \varepsilon}}\big)$ that returns a cycle of length at most $ 2\ell \left\lceil \frac{g}{2} \right\rceil - 2 \left\lfloor \varepsilon \left\lceil \frac{g}{2} \right\rceil \right\rfloor, $ where $\ell \geq 2$ is an integer and $\varepsil…

A 0.51-Approximation of Maximum Matching in Sublinear $n^{1.5}$ Time
Sepideh Mahabadi, Mohammad Roghani, Jakub Tarnawski
https://arxiv.org/abs/2506.01669 h…

A 0.51-Approximation of Maximum Matching in Sublinear $n^{1.5}$ Time
We study the problem of estimating the size of a maximum matching in sublinear time. The problem has been studied extensively in the literature and various algorithms and lower bounds are known for it. Our result is a $0.5109$-approximation algorithm with a running time of $\tilde{O}(n\sqrt{n})$. All previous algorithms either provide only a marginal improvement (e.g., $2^{-280}$) over the $0.5$-approximation that arises from estimating a \emph{maximal} matching, or have a running time that i…

How Israel’s Operation Rising Lion Dismantled Iran from Within: A Case Study in the Art of Deception | Hudson Institute
#Israel #Palestine #Zionism #OODA #Iran

Nearly-Linear Time Private Hypothesis Selection with the Optimal Approximation Factor
Maryam Aliakbarpour, Zhan Shi, Ria Stevens, Vincent X. Wang
https://arxiv.org/abs/2506.01162 …

Nearly-Linear Time Private Hypothesis Selection with the Optimal Approximation Factor
Estimating the density of a distribution from its samples is a fundamental problem in statistics. Hypothesis selection addresses the setting where, in addition to a sample set, we are given $n$ candidate distributions -- referred to as hypotheses -- and the goal is to determine which one best describes the underlying data distribution. This problem is known to be solvable very efficiently, requiring roughly $O(\log n)$ samples and running in $\tilde{O}(n)$ time. The quality of the output is mea…

Fast Algorithms for Graph Arboricity and Related Problems
Ruoxu Cen, Henry Fleischmann, George Z. Li, Jason Li, Debmalya Panigrahi
https://arxiv.org/abs/2507.15598

Fast Algorithms for Graph Arboricity and Related Problems
We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of $\tilde{O}(nm)$ for weighted graphs and $\tilde{O}(m^{3/2}) $ for unweighted graphs (Gabow 1995) for this problem. The running time of our algorithm is dominated by a logarithmic number of calls to a directed global minimum cut subroutine -- if the running t…

Towards practical FPRAS for #NFA: Exploiting the Power of Dependence
Kuldeep S. Meel, Alexis de Colnet
https://arxiv.org/abs/2506.23561

Towards practical FPRAS for #NFA: Exploiting the Power of Dependence
#NFA refers to the problem of counting the words of length $n$ accepted by a non-deterministic finite automaton. #NFA is #P-hard, and although fully-polynomial-time randomized approximation schemes (FPRAS) exist, they are all impractical. The first FPRAS for #NFA had a running time of $\tilde{O}(n^{17}m^{17}\varepsilon^{-14}\log(δ^{-1}))$, where $m$ is the number of states in the automaton, $δ\in (0,1]$ is the confidence parameter, and $\varepsilon > 0$ is the tolerance parameter (typically s…

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure
Micha{\l} Derezi\'nski, Aaron Sidford
https://arxiv.org/abs/2507.11724 …

Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure
We provide new high-accuracy randomized algorithms for solving linear systems and regression problems that are well-conditioned except for $k$ large singular values. For solving such $d \times d$ positive definite system our algorithms succeed whp. and run in time $\tilde O(d^2 + k^ω)$. For solving such regression problems in a matrix $\mathbf{A} \in \mathbb{R}^{n \times d}$ our methods succeed whp. and run in time $\tilde O(\mathrm{nnz}(\mathbf{A}) + d^2 + k^ω)$ where $ω$ is the matrix mult…

On Tight Robust Coresets for $k$-Medians Clustering
Lingxiao Huang, Zhenyu Jiang, Yi Li, Xuan Wu
https://arxiv.org/abs/2507.11260 https://

On Tight Robust Coresets for $k$-Medians Clustering
This paper considers coresets for the robust $k$-medians problem with $m$ outliers, and new constructions in various metric spaces are obtained. Specifically, for metric spaces with a bounded VC or doubling dimension $d$, the coreset size is $O(m) + \tilde{O}(kd\varepsilon^{-2})$, which is optimal up to logarithmic factors. For Euclidean spaces, the coreset size is $O(m\varepsilon^{-1}) + \tilde{O}(\min\{k^{4/3}\varepsilon^{-2},k\varepsilon^{-3}\})$, improving upon a recent result by Jiang and …

All-Pairs Shortest Paths with Few Weights per Node
Amir Abboud, Nick Fischer, Ce Jin, Virginia Vassilevska Williams, Zoe Xi
https://arxiv.org/abs/2506.20017

All-Pairs Shortest Paths with Few Weights per Node
We study the central All-Pairs Shortest Paths (APSP) problem under the restriction that there are at most $d$ distinct weights on the outgoing edges from every node. For $d=n$ this is the classical (unrestricted) APSP problem that is hypothesized to require cubic time $n^{3-o(1)}$, and at the other extreme, for $d=1$, it is equivalent to the Node-Weighted APSP problem. We present new algorithms that achieve the following results: 1. Node-Weighted APSP can be solved in time $\tilde{O}(n^{(3+ω…

Tight simulation of a distribution using conditional samples
Tomer Adar
https://arxiv.org/abs/2506.18444 https://arxiv.org/pdf/2506.1…

Tight simulation of a distribution using conditional samples
We present an algorithm for simulating a distribution using prefix conditional samples (Adar, Fischer and Levi, 2024), as well as ``prefix-compatible'' conditional models such as the interval model (Cannone, Ron and Servedio, 2015) and the subcube model (CRS15, Bhattacharyya and Chakraborty, 2018). The conditional sample complexity is $O(\log^2 N / \varepsilon^2)$ prefix conditional samples per query, which improves on the previously known $\tilde{O}(\log^3 N / \varepsilon^2)$ (Kumar, Meel and …

Optimal Pure Differentially Private Sparse Histograms in Near-Linear Deterministic Time
Florian Kerschbaum, Steven Lee, Hao Wu
https://arxiv.org/abs/2507.17017 https://

Optimal Pure Differentially Private Sparse Histograms in Near-Linear Deterministic Time
We introduce an algorithm that releases a pure differentially private sparse histogram over $n$ participants drawn from a domain of size $d \gg n$. Our method attains the optimal $\ell_\infty$-estimation error and runs in strictly $O(n \ln \ln d)$ time in the word-RAM model, thereby improving upon the previous best known deterministic-time bound of $\tilde{O}(n^2)$ and resolving the open problem of breaking this quadratic barrier (Balcer and Vadhan, 2019). Central to our algorithm is a novel pr…

Quantum Pattern Matching with Wildcards
Masoud Seddighin, Saeed Seddighin
https://arxiv.org/abs/2507.13885 https://arxiv.org/pdf/2507…

Quantum Pattern Matching with Wildcards
Pattern matching is one of the fundamental problems in Computer Science. Both the classic version of the problem as well as the more sophisticated version where wildcards can also appear in the input can be solved in almost linear time $\tilde O(n)$ using the KMP algorithm and Fast Fourier Transform, respectively. In 2000, Ramesh and Vinay~\cite{ramesh2003string} give a quantum algorithm that solves classic pattern matching in sublinear time and asked whether the wildcard problem can also be so…

To buy or not to buy: deterministic rent-or-buy problems on node-weighted graphs
Sander Borst, Moritz Venzin
https://arxiv.org/abs/2507.08698 https://

To buy or not to buy: deterministic rent-or-buy problems on node-weighted graphs
We study the rent-or-buy variant of the online Steiner forest problem on node- and edge-weighted graphs. For $n$-node graphs with at most $\bar{n}$ non-zero node-weights, and at most $\tilde{k}$ different arriving terminal pairs, we obtain a deterministic, $O(\log n \log \bar{n})$-competitive algorithm. This improves on the previous best, $O(\log^4 n)$-competitive algorithm obtained by the black-box reduction from (Bartal et al. 2021) combined with the previously best deterministic algorithms f…