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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1112.0520","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-12-02T17:50:10Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"b72eba9ff44051681d2f98f69db6ce358e3c4c316fc49826744e0520221bce8c","abstract_canon_sha256":"84d0a4a7f361750837c6b8683cc8d5e9b011e2850db3bdf0abc76f69d65bf53d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:06.364760Z","signature_b64":"cIYt04pnQr0Nzrh8X0FpWzCKR/DnNdBDgNr3J7RDY29zKWX/Z0aZ7aOi1N2Y/Ckq98LAh80FwlY3h8BjBwxuDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02187101a947df9bf428c487d89b24cdf767531fc2906280a46edda016732c43","last_reissued_at":"2026-05-18T04:04:06.364153Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:06.364153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $a_1\\le a_2\\le ...\\le a_n$. 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