{"paper":{"title":"A Nearly Tight Lower Bound for the $d$-Dimensional Cow-Path Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"John Kuszmaul, Nikhil Bansal, William Kuszmaul","submitted_at":"2022-09-17T23:37:21Z","abstract_excerpt":"In the $d$-dimensional cow-path problem, a cow living in $\\mathbb{R}^d$ must locate a $(d - 1)$-dimensional hyperplane $H$ whose location is unknown. The only way that the cow can find $H$ is to roam $\\mathbb{R}^d$ until it intersects $\\mathcal{H}$. If the cow travels a total distance $s$ to locate a hyperplane $H$ whose distance from the origin was $r \\ge 1$, then the cow is said to achieve competitive ratio $s / r$.\n  It is a classic result that, in $\\mathbb{R}^2$, the optimal (deterministic) competitive ratio is $9$. In $\\mathbb{R}^3$, the optimal competitive ratio is known to be at most $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.08427","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.08427/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}