{"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/linear-search-with-probabilistic-detection","title":"Linear Search with Probabilistic Detection and Variable Speeds","arxiv_id":"2505.09429","date":"2025-05-14","proceeding":null,"authors":["Jared Coleman","Oscar Morales-Ponce"],"abstract":"We present results on new variants of the famous linear search (or cow-path) problem that involves an agent searching for a target with unknown position on the infinite line. We consider the variant where the agent can move either at speed $1$ or at a slower speed $v \\in [0, 1)$. When traveling at the slower speed $v$, the agent is guaranteed to detect the target upon passing through its location. When traveling at speed $1$, however, the agent, upon passing through the target's location, detects it with probability $p \\in [0, 1]$. We present algorithms and provide upper bounds for the competitive ratios for three cases separately: when $p=0$, $v=0$, and when $p,v \\in (0,1)$. We also prove that the provided algorithm for the $p=0$ case is optimal.","url_abs":"https://arxiv.org/abs/2505.09429v1","url_pdf":"https://arxiv.org/pdf/2505.09429v1.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":"linear-search-with-probabilistic-detection","repo_url":"https://github.com/kubishi/code_multi_speed_cow","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"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}