{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/just-take-the-average-an-embarrassingly","title":"Just Take the Average! An Embarrassingly Simple $2^n$-Time Algorithm for SVP (and CVP)","arxiv_id":"1709.01535","date":"2017-09-05","proceeding":null,"authors":["Divesh Aggarwal","Noah Stephens-Davidowitz"],"abstract":"We show a $2^{n+o(n)}$-time (and space) algorithm for the Shortest Vector Problem on lattices (SVP) that works by repeatedly running an embarrassingly simple \"pair and average\" sieving-like procedure on a list of lattice vectors. This matches the running time (and space) of the current fastest known algorithm, due to Aggarwal, Dadush, Regev, and Stephens-Davidowitz (ADRS, in STOC, 2015), with a far simpler algorithm. Our algorithm is in fact a modification of the ADRS algorithm, with a certain careful rejection sampling step removed. The correctness of our algorithm follows from a more general \"meta-theorem,\" showing that such rejection sampling steps are unnecessary for a certain class of algorithms and use cases. In particular, this also applies to the related $2^{n + o(n)}$-time algorithm for the Closest Vector Problem (CVP), due to Aggarwal, Dadush, and Stephens-Davidowitz (ADS, in FOCS, 2015), yielding a similar embarrassingly simple algorithm for $\\gamma$-approximate CVP for any $\\gamma = 1+2^{-o(n/\\log n)}$. (We can also remove the rejection sampling procedure from the $2^{n+o(n)}$-time ADS algorithm for exact CVP, but the resulting algorithm is still quite complicated.)","url_abs":"https://arxiv.org/abs/1709.01535v1","url_pdf":"https://arxiv.org/pdf/1709.01535v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"just-take-the-average-an-embarrassingly","repo_url":"https://github.com/oliver-leung/as18","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}