{"paper":{"title":"Clustered Integer 3SUM via Additive Combinatorics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Moshe Lewenstein, Timothy M. Chan","submitted_at":"2015-02-18T12:49:06Z","abstract_excerpt":"We present a collection of new results on problems related to 3SUM, including:\n  1. The first truly subquadratic algorithm for\n  $\\ \\ \\ \\ \\ $ 1a. computing the (min,+) convolution for monotone increasing sequences with integer values bounded by $O(n)$,\n  $\\ \\ \\ \\ \\ $1b. solving 3SUM for monotone sets in 2D with integer coordinates bounded by $O(n)$, and\n  $\\ \\ \\ \\ \\ $1c. preprocessing a binary string for histogram indexing (also called jumbled indexing).\n  The running time is: $O(n^{(9+\\sqrt{177})/12}\\,\\textrm{polylog}\\,n)=O(n^{1.859})$ with randomization, or $O(n^{1.864})$ deterministically. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05204","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"}