cs.DS · 2026-08-18 · No. 88

Data Structures and Algorithms, 2026-08-18.

3 new papers in cs.DS. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

3 entries
  1. 01

    Improving the matrix multiplication exponent with modern optimization and AlphaEvolve

    Emilien Dupont, Marvin Eisenberger, Borislav Kozlovskii, Abbas Mehrabian, Francisco J. R. Ruiz, Abigail See, Renfei...

    cs.DS · cs.AI · cs.CC · cs.LG

    The current best bounds on the matrix multiplication exponent $ω$ are obtained through a refinement of the laser method called combination loss analysis (Duan et al., 2022; Williams et al., 2024; Alman et al., 2025). In this note, we address the optimization problem at the core of this approach and propose several improvements. First, we reformulate the optimization problem allowing us to solve it in a larger setting than was previously...

    arxiv.org/abs/2608.16884 · PDF

  2. 02

    Spectral Gaps of Hit-and-Run and Coordinate Hit-and-Run

    Yunbum Kook, Santosh S. Vempala

    cs.DS · cs.LG · math.PR · math.ST

    For any convex body $\mathcal{K}\subset\mathbb{R}^{n}$ containing a unit ball, the spectral gap of Hit-and-Run is $Ω(1/(n^2 C_{\mathsf{PI}}))$, where $C_{\mathsf{PI}}$ is the Poincaré constant of the uniform distribution $π$ over $\mathcal{K}$. This implies that Hit-and-Run converges to a distribution within $χ^2$-divergence $\varepsilon$ of the uniform distribution $π$ in $O(n^2 C_{\mathsf{PI}}\log(M/\varepsilon))$ steps from any starting...

    arxiv.org/abs/2608.16878 · PDF

  3. 03

    Correlation Clustering with Random Partial Information

    Rajath Rao K. N., Jens Schlöter, Sami Davies, Amira Ouchene, Yasamin Nazari

    cs.DS · cs.LG

    Correlation clustering is a fundamental unsupervised learning problem. On complete graphs, both the min-disagreement and min-max objectives admit constant-factor approximations, yet on general (non-complete) graphs, the best guarantees blow up to $O(\log n)$ and $O(\sqrt{n})$. This gap between the two regimes motivates the following question: are there classes of incomplete graphs that circumvent the lower bounds on general graphs and admit...

    arxiv.org/abs/2608.16315 · PDF

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