{"paper":{"title":"On the Complexity of Approximate Sum of Sorted List","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Bin Fu","submitted_at":"2011-12-02T17:50:10Z","abstract_excerpt":"We consider the complexity for computing the approximate sum $a_1+a_2+...+a_n$ of a sorted list of numbers $a_1\\le a_2\\le ...\\le a_n$. We show an algorithm that computes an $(1+\\epsilon)$-approximation for the sum of a sorted list of nonnegative numbers in an $O({1\\over \\epsilon}\\min(\\log n, {\\log ({x_{max}\\over x_{min}})})\\cdot (\\log {1\\over \\epsilon}+\\log\\log n))$ time, where $x_{max}$ and $x_{min}$ are the largest and the least positive elements of the input list, respectively. We prove a lower bound $\\Omega(\\min(\\log n,\\log ({x_{max}\\over x_{min}}))$ time for every O(1)-approximation algor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0520","kind":"arxiv","version":4},"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"}