{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:FIIPBXFWETHQPMC55WFVYXVR3L","short_pith_number":"pith:FIIPBXFW","schema_version":"1.0","canonical_sha256":"2a10f0dcb624cf07b05ded8b5c5eb1daf513d9894c08476c1b5bc42d82156cc0","source":{"kind":"arxiv","id":"2008.05106","version":3},"attestation_state":"computed","paper":{"title":"Settling SETH vs. Approximate Sparse Directed Unweighted Diameter (up to (NU)NSETH)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ray Li","submitted_at":"2020-08-12T04:43:01Z","abstract_excerpt":"We prove several tight results on the fine-grained complexity of approximating the diameter of a graph. First, we prove that, for any $\\varepsilon>0$, assuming the Strong Exponential Time Hypothesis (SETH), there are no near-linear time $2-\\varepsilon$-approximation algorithms for the Diameter of a sparse directed graph, even in unweighted graphs. This result shows that a simple near-linear time 2-approximation algorithm for Diameter is optimal under SETH, answering a question from a survey of Rubinstein and Vassilevska-Williams (SIGACT '19) for the case of directed graphs.\n  In the same surve"},"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":"2008.05106","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-08-12T04:43:01Z","cross_cats_sorted":[],"title_canon_sha256":"fb3d306ae2552655941da3d2c581b334f176a95ed26c6d4dc9601bdd471b3942","abstract_canon_sha256":"63ff32b99054879437e7361967e1470c83a358848a8569cde98a46bbbb7a5906"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:28:32.243331Z","signature_b64":"6/x/w6JNb/bwYIjCH0W47KtTgedpXQQshAJrOWv28AiUuXG6qhl4h4vtaAiDuO0DOf3qQ1D/ZHV/MP3BSWIMBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a10f0dcb624cf07b05ded8b5c5eb1daf513d9894c08476c1b5bc42d82156cc0","last_reissued_at":"2026-07-05T02:28:32.242906Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:28:32.242906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Settling SETH vs. Approximate Sparse Directed Unweighted Diameter (up to (NU)NSETH)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ray Li","submitted_at":"2020-08-12T04:43:01Z","abstract_excerpt":"We prove several tight results on the fine-grained complexity of approximating the diameter of a graph. First, we prove that, for any $\\varepsilon>0$, assuming the Strong Exponential Time Hypothesis (SETH), there are no near-linear time $2-\\varepsilon$-approximation algorithms for the Diameter of a sparse directed graph, even in unweighted graphs. This result shows that a simple near-linear time 2-approximation algorithm for Diameter is optimal under SETH, answering a question from a survey of Rubinstein and Vassilevska-Williams (SIGACT '19) for the case of directed graphs.\n  In the same surve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.05106","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.05106/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2008.05106","created_at":"2026-07-05T02:28:32.242978+00:00"},{"alias_kind":"arxiv_version","alias_value":"2008.05106v3","created_at":"2026-07-05T02:28:32.242978+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.05106","created_at":"2026-07-05T02:28:32.242978+00:00"},{"alias_kind":"pith_short_12","alias_value":"FIIPBXFWETHQ","created_at":"2026-07-05T02:28:32.242978+00:00"},{"alias_kind":"pith_short_16","alias_value":"FIIPBXFWETHQPMC5","created_at":"2026-07-05T02:28:32.242978+00:00"},{"alias_kind":"pith_short_8","alias_value":"FIIPBXFW","created_at":"2026-07-05T02:28:32.242978+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FIIPBXFWETHQPMC55WFVYXVR3L","json":"https://pith.science/pith/FIIPBXFWETHQPMC55WFVYXVR3L.json","graph_json":"https://pith.science/api/pith-number/FIIPBXFWETHQPMC55WFVYXVR3L/graph.json","events_json":"https://pith.science/api/pith-number/FIIPBXFWETHQPMC55WFVYXVR3L/events.json","paper":"https://pith.science/paper/FIIPBXFW"},"agent_actions":{"view_html":"https://pith.science/pith/FIIPBXFWETHQPMC55WFVYXVR3L","download_json":"https://pith.science/pith/FIIPBXFWETHQPMC55WFVYXVR3L.json","view_paper":"https://pith.science/paper/FIIPBXFW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2008.05106&json=true","fetch_graph":"https://pith.science/api/pith-number/FIIPBXFWETHQPMC55WFVYXVR3L/graph.json","fetch_events":"https://pith.science/api/pith-number/FIIPBXFWETHQPMC55WFVYXVR3L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FIIPBXFWETHQPMC55WFVYXVR3L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FIIPBXFWETHQPMC55WFVYXVR3L/action/storage_attestation","attest_author":"https://pith.science/pith/FIIPBXFWETHQPMC55WFVYXVR3L/action/author_attestation","sign_citation":"https://pith.science/pith/FIIPBXFWETHQPMC55WFVYXVR3L/action/citation_signature","submit_replication":"https://pith.science/pith/FIIPBXFWETHQPMC55WFVYXVR3L/action/replication_record"}},"created_at":"2026-07-05T02:28:32.242978+00:00","updated_at":"2026-07-05T02:28:32.242978+00:00"}