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Math paper: Sorted projections determine n points in k dimensions

By PulseAugur Editorial · [1 sources] ·

A new paper explores the mathematical problem of determining the number of sorted projections needed to uniquely identify a set of points in k-dimensional space. Researchers have established bounds, showing that more than (k-1)log2(n) directions are always required, while (k-1)n+1 directions are sufficient. The paper refines these bounds, demonstrating that for higher dimensions, a specific logarithmic number of directions is adequate, improving upon previous linear bounds for certain point set sizes. AI

RANK_REASON This is a research paper published on arXiv concerning a mathematical problem. [lever_c_demoted from research: ic=1 ai=0.1]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Math paper: Sorted projections determine n points in k dimensions

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This is a research paper published on arXiv concerning a mathematical problem. [lever_c_demoted from research: ic=1 ai=0.1]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Christopher Gorham Lester, Raymond Hau S{\o}rensen ·

    How many sorted projections determine n points in k dimensions?

    arXiv:2611.06470v1 Announce Type: cross Abstract: Let $d_1,\dots,d_m$ be directions in $\mathbb{R}^k$, where $k\ge 2$. A multiset $X$ of $n$ points of $\mathbb{R}^k$ projects to the $m$ multisets of numbers $\{\{x\cdot d_j : x\in X\}\}$, or equivalently to the $m$ sorted lists of…

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