{"paper":{"title":"An approximation notion between P and FPTAS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A new approximation notion for NP-hard problems is strictly stronger than FPTAS but weaker than polynomial-time solvability.","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Erel Segal-Halevi, Samuel Bismuth","submitted_at":"2026-03-18T08:55:02Z","abstract_excerpt":"We present an approximation notion for NP-hard optimization problems. The notion is based on an *amortized relaxation*: the relaxed optimum of an input is the largest per-copy value attainable when many copies of the input are solved together. We prove that (assuming P != NP) the new notion is strictly stronger than FPTAS, but strictly weaker than having a polynomial-time algorithm. Our results introduce a new computational complexity class for optimization problems, which is a strict superset of P and a strict subset of FPTAS."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that (assuming P != NP) the new notion is strictly stronger than FPTAS, but strictly weaker than having a polynomial-time algorithm.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The optimization problems must be representable by binary functions, and the standard assumption P ≠ NP must hold for the strict separation to be meaningful.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A new approximation notion for binary-function NP-hard problems is strictly stronger than FPTAS yet strictly weaker than polynomial-time algorithms, assuming P ≠ NP.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A new approximation notion for NP-hard problems is strictly stronger than FPTAS but weaker than polynomial-time solvability.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b35ce977e41160d59580a25ea7c2dff20e97cd7e011e9f2b29bcefe0739941af"},"source":{"id":"2603.17489","kind":"arxiv","version":4},"verdict":{"id":"0a0f9f40-c82a-4b9d-81d1-44b8076d1ee4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T08:48:25.598755Z","strongest_claim":"We prove that (assuming P != NP) the new notion is strictly stronger than FPTAS, but strictly weaker than having a polynomial-time algorithm.","one_line_summary":"A new approximation notion for binary-function NP-hard problems is strictly stronger than FPTAS yet strictly weaker than polynomial-time algorithms, assuming P ≠ NP.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The optimization problems must be representable by binary functions, and the standard assumption P ≠ NP must hold for the strict separation to be meaningful.","pith_extraction_headline":"A new approximation notion for NP-hard problems is strictly stronger than FPTAS but weaker than polynomial-time solvability."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.17489/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}