cs.DS · 2026-08-04 · No. 74

Data Structures and Algorithms, 2026-08-04.

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

01 — The papers

2 entries
  1. 01

    The Condition-Number Barrier in Sparse Least Squares

    Honghao Lin, Vahab Mirrokni, David P. Woodruff

    cs.DS · cs.LG

    In [AS21], Axiotis and Sviridenko conjectured that the linear dependence on the restricted condition number in sparse convex optimization cannot be improved by a polynomial-time algorithm. We establish their conjectured lower bound for least-squares objectives, conditional on the randomized exact-volume Small-Set Expansion Hypothesis in the weighted regular-graph formulation of Raghavendra, Steurer, and Tulsiani [RST12]. Concretely, for every...

    arxiv.org/abs/2608.02588 · PDF

  2. 02

    Randomized Algorithms for Learning Partitions with Near Optimal Query Complexity in Constant Rounds

    Deeparnab Chakrabarty, Aditi Dudeja, David Saulpic

    cs.DS · cs.LG

    We study the round complexity of learning a hidden partition $\mathcal{P}$ of an $n$-element universe using PAIR queries: PAIR($x,y$) tells us whether $x$ and $y$ belong to the same part of the partition or not. While it is easy to learn using $n|\mathcal{P}|$ queries using a basic algorithm and this query complexity is optimal, this basic algorithm is highly sequential. Black, Mazumdar, and Saha [COLT 2025] recently gave tight deterministic...

    arxiv.org/abs/2608.02176 · PDF

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