{"paper":{"title":"The Strong 3SUM-INDEXING Conjecture is False","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ely Porat, Tsvi Kopelowitz","submitted_at":"2019-07-25T17:11:11Z","abstract_excerpt":"In the 3SUM-Indexing problem the goal is to preprocess two lists of elements from $U$, $A=(a_1,a_2,\\ldots,a_n)$ and $B=(b_1,b_2,...,b_n)$, such that given an element $c\\in U$ one can quickly determine whether there exists a pair $(a,b)\\in A \\times B$ where $a+b=c$. Goldstein et al.~[WADS'2017] conjectured that there is no algorithm for 3SUM-Indexing which uses $n^{2-\\Omega(1)}$ space and $n^{1-\\Omega(1)}$ query time.\n  We show that the conjecture is false by reducing the 3SUM-Indexing problem to the problem of inverting functions, and then applying an algorithm of Fiat and Naor [SICOMP'1999] f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11206","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"}