algorithms

MIT Press's 634-page book "Algorithms for Optimization" is available as a free CC-BY-NC-ND PDF, with the second edition (featuring Julia implementations and new chapters on DCP, surrogate models, and multidisciplinary optimization) releasing January 5, 2027.

An essay tracing how 'programs' evolved from TV broadcasts to today's code-driven recommendation algorithms, arguing that widespread media literacy and programming education are lacking while platforms increasingly shape prices and perception.

A technical blog essay tracing the history of trying to rigorously define algorithmic efficiency, from Jack Edmonds' 1965 blossom algorithm and his notion of a 'good' algorithm to the Exponential Time Hypothesis, arguing complexity theory lost sight of the original practical problems.

Major League Baseball is shifting its social media strategy from stats-and-highlights content to fandom-culture edits — like highlight reels set to Olivia Rodrigo songs — to reach younger, more casual fans as recommendation algorithms reshape how content is discovered.

OpenAI and Anthropic both claim their internal AI models independently refuted the Exponential Time Hypothesis by solving 3-SAT in 2^o(n) time, a result with Lean certificates but not yet reviewed by human experts. The article is a 43-minute explainer covering the two proofs, their galactic runtime, and how to read such claims.

A 2023 paper presenting a stackless approach to automating the flood fill algorithm, describing techniques that avoid an explicit stack during region filling. The linked PDF content did not render, so the summary is inferred from the title.

OpenAI 宣称发布了一篇证明指数时间假设（ETH）为假的论文，主定理已通过 Lean 验证，并由 Impagliazzo、Paturi 和 Williams 领导的独立工作组进行审查；文章通俗解释了 3-SAT、NP 完全性以及 ETH 被证伪可能带来的深远影响。

A blog post introducing a new fast algorithm for signed 64-bit floor division by compile-time constants, benchmarked 10–20% faster than existing approaches on ARM and ~5–10% faster on most x86 cases, along with a copy-paste code generator and a critique of how compilers and libraries handle floor division.

cp-algorithms 上关于 Treap（笛卡尔树）的算法文档，介绍了这种结合二叉搜索树与二叉堆特性的随机化数据结构及其插入、删除、合并等操作的复杂度与实现思路。

David Harvey and Joris van der Hoeven's paper presenting a groundbreaking O(n log n) integer multiplication algorithm, breaking the long-standing complexity barrier for multiplying large integers.

A community research repository reports a sharper exponent bound for integer multiplication, achieving T(n)=O(n(log n)^(1-κ)) with κ=0.0023 under the OpenAI #109 framework, conditional on unverified hypotheses and not yet a complete Lean proof.

一篇介绍用 Swift 实现超高速 IPv4 地址解析算法的博客，通过新算法在 Apple M6 上以约 3 纳秒、15 个 CPU 周期完成解析，成果将贡献给 Swift 官方的 swift-networking-types 项目。

A 2014 blog post by L. Pereira exploring increasingly optimized ways to convert integers to strings in C, comparing naive division-based approaches, an in-place reverse-free variant used in Lwan, and Facebook's pair-of-digits lookup table trick that roughly halves the number of divisions for a ~31% speedup.

一篇技术评论文章，批评 OpenAI 在数学论文集中声称的更快快速傅里叶变换（FFT）算法，指出其改进微乎其微，更像是利用理论模型在硬件上并不实际可行的“恶意利用”，而非真正的突破。

An automated research run exploring integer multiplication algorithms with complexity below n log n, providing reproducible contributions, a repository contribution guide, and interactive visualization of ideas and pull requests.

纽约州在对 TikTok 的诉讼中新增指控，称 TikTok 向数千名用户（包括儿童和青少年）提供‘安慰剂’版本的安全功能，如算法重置功能实际无效，误导用户以为已生效。

Eric Lippert's new Manning book "Fabulous Adventures in Data Structures and Algorithms" has become a top new release on Amazon, covering immutable data structures, DAWGs, compiler design, and Bayesian techniques relevant to AI.

An internal Anthropic Claude model discovered the first truly subquadratic 3SUM algorithm (O(n^1.9992)) and truly subcubic APSP algorithm (O(n^2.9995)), refuting the long-standing 3SUM and APSP hypotheses in fine-grained complexity theory. The result, formalized in a paper by Josh Alman and Virginia Vassilevska Williams, stems from a new thin matrix multiplication algorithm and was verified using Lean 4.

This paper introduces AlgoREval, a benchmark of 599 problems covering 77 classical algorithms across 14 domains, 7 languages, and 4 graph-input representations, to measure LLMs' ability to reproduce well-known algorithms as 'parametric code retrieval' rather than true synthesis. Across 15 models (7B–34B), accuracy varies widely by language and input format, and the authors caution against deploying AI-generated algorithmic code without systematic validation.

FlashSinkhorn 2 introduces a two-stage block-sparse GPU solver for entropic optimal transport that scales to 1.34e8-particle point clouds, solving them on a single A100 to a marginal residual below 0.01 in under 2.5 hours — claimed to be the largest discrete EOT problem solved at this accuracy within hours. An open-source implementation is released.