{"paper":{"title":"An Illuminating Algorithm for the Light Bulb Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Josh Alman","submitted_at":"2018-10-15T22:51:50Z","abstract_excerpt":"The Light Bulb Problem is one of the most basic problems in data analysis. One is given as input $n$ vectors in $\\{-1,1\\}^d$, which are all independently and uniformly random, except for a planted pair of vectors with inner product at least $\\rho \\cdot d$ for some constant $\\rho > 0$. The task is to find the planted pair. The most straightforward algorithm leads to a runtime of $\\Omega(n^2)$. Algorithms based on techniques like Locality-Sensitive Hashing achieve runtimes of $n^{2 - O(\\rho)}$; as $\\rho$ gets small, these approach quadratic.\n  Building on prior work, we give a new algorithm for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06740","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":""},"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"}