{"paper":{"title":"The Impossibility of Simultaneous Time and I/O Optimality for The Planar Maxima and Convex Hull Problems","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"No deterministic output-sensitive algorithm achieves both optimal time and optimal I/O for planar convex hull and maxima.","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Gerth St{\\o}lting Brodal, Nodari Sitchinava, Peyman Afshani","submitted_at":"2026-05-10T10:31:45Z","abstract_excerpt":"We prove that no deterministic output-sensitive algorithm for the planar convex hull and maxima problems can obtain both optimal time and I/O complexity, where the optimality is defined with respect to both the input and output sizes. This explains why the best previous algorithms achieved an optimal I/O bound at the cost of sub-optimal running time (Goodrich et al. [FOCS, 1993]). To the best of our knowledge, the impossibility of simultaneous optimality was only shown previously for the permutation problem by Brodal and Fagerberg [STOC, 2003]. Our results imply that no optimal deterministic o"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that no deterministic output-sensitive algorithm for the planar convex hull and maxima problems can obtain both optimal time and I/O complexity, where the optimality is defined with respect to both the input and output sizes.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The lower bound holds in the standard external-memory model where time and I/O complexities are measured separately and optimality is defined with respect to input size n and output size h.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"No deterministic output-sensitive algorithm for planar maxima or convex hull can simultaneously achieve optimal time and I/O complexity.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"No deterministic output-sensitive algorithm achieves both optimal time and optimal I/O for planar convex hull and maxima.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"51cb7be529084b534fe032341dfedab1dba114675e6f5d8d57f048ec4756c492"},"source":{"id":"2605.09464","kind":"arxiv","version":2},"verdict":{"id":"278d871b-3bc3-4964-af56-19040685a1ee","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T04:35:02.142354Z","strongest_claim":"We prove that no deterministic output-sensitive algorithm for the planar convex hull and maxima problems can obtain both optimal time and I/O complexity, where the optimality is defined with respect to both the input and output sizes.","one_line_summary":"No deterministic output-sensitive algorithm for planar maxima or convex hull can simultaneously achieve optimal time and I/O complexity.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The lower bound holds in the standard external-memory model where time and I/O complexities are measured separately and optimality is defined with respect to input size n and output size h.","pith_extraction_headline":"No deterministic output-sensitive algorithm achieves both optimal time and optimal I/O for planar convex hull and maxima."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.09464/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T07:42:01.423220Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T19:35:13.755092Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T13:01:17.996977Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T10:11:41.179681Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"74f454eeddb162c018a29289af0dd7fb16f39c83ac937b4dcaa29baeaf546654"},"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"}