{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ZY737SK5W5BZNPXEYJFAV6WDUI","short_pith_number":"pith:ZY737SK5","schema_version":"1.0","canonical_sha256":"ce3fbfc95db74396bee4c24a0afac3a215c28065d0149e6fa8a3f6b962fe9e57","source":{"kind":"arxiv","id":"1606.08141","version":1},"attestation_state":"computed","paper":{"title":"Minimum Fill-In: Inapproximability and Almost Tight Lower Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"R. B. Sandeep, Yixin Cao","submitted_at":"2016-06-27T07:02:18Z","abstract_excerpt":"Given an $n*n$ sparse symmetric matrix with $m$ nonzero entries, performing Gaussian elimination may turn some zeroes into nonzero values. To maintain the matrix sparse, we would like to minimize the number $k$ of these changes, hence called the minimum fill-in problem. Agrawal et al.~[FOCS'90] developed the first approximation algorithm, based on early heuristics by George [SIAM J Numer Anal 10] and by Lipton et al.~[SIAM J Numer Anal 16]. The objective function they used is $m+k$, the number of nonzero elements after elimination. An approximation algorithm using $k$ as the objective function"},"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":"1606.08141","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-06-27T07:02:18Z","cross_cats_sorted":[],"title_canon_sha256":"6402be6ca2819411f59486f221023365809461946759f35797bb0c8c9d85b969","abstract_canon_sha256":"0d561da23bf0ab213a80e43029c4e801e0b24079780cb79b4e5c20dcd2234671"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:52.679274Z","signature_b64":"d4Io/r4Mscz4MymjB11i4flwoYpRtYMPTbsOeIlPpfxOJmb/EvTA1do+OwWBxZH7IDyWqj79LbtW1vt3FP5HDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce3fbfc95db74396bee4c24a0afac3a215c28065d0149e6fa8a3f6b962fe9e57","last_reissued_at":"2026-05-18T01:11:52.678656Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:52.678656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimum Fill-In: Inapproximability and Almost Tight Lower Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"R. B. Sandeep, Yixin Cao","submitted_at":"2016-06-27T07:02:18Z","abstract_excerpt":"Given an $n*n$ sparse symmetric matrix with $m$ nonzero entries, performing Gaussian elimination may turn some zeroes into nonzero values. To maintain the matrix sparse, we would like to minimize the number $k$ of these changes, hence called the minimum fill-in problem. Agrawal et al.~[FOCS'90] developed the first approximation algorithm, based on early heuristics by George [SIAM J Numer Anal 10] and by Lipton et al.~[SIAM J Numer Anal 16]. The objective function they used is $m+k$, the number of nonzero elements after elimination. An approximation algorithm using $k$ as the objective function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08141","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1606.08141","created_at":"2026-05-18T01:11:52.678760+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.08141v1","created_at":"2026-05-18T01:11:52.678760+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08141","created_at":"2026-05-18T01:11:52.678760+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZY737SK5W5BZ","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZY737SK5W5BZNPXE","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZY737SK5","created_at":"2026-05-18T12:30:55.937587+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/ZY737SK5W5BZNPXEYJFAV6WDUI","json":"https://pith.science/pith/ZY737SK5W5BZNPXEYJFAV6WDUI.json","graph_json":"https://pith.science/api/pith-number/ZY737SK5W5BZNPXEYJFAV6WDUI/graph.json","events_json":"https://pith.science/api/pith-number/ZY737SK5W5BZNPXEYJFAV6WDUI/events.json","paper":"https://pith.science/paper/ZY737SK5"},"agent_actions":{"view_html":"https://pith.science/pith/ZY737SK5W5BZNPXEYJFAV6WDUI","download_json":"https://pith.science/pith/ZY737SK5W5BZNPXEYJFAV6WDUI.json","view_paper":"https://pith.science/paper/ZY737SK5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.08141&json=true","fetch_graph":"https://pith.science/api/pith-number/ZY737SK5W5BZNPXEYJFAV6WDUI/graph.json","fetch_events":"https://pith.science/api/pith-number/ZY737SK5W5BZNPXEYJFAV6WDUI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZY737SK5W5BZNPXEYJFAV6WDUI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZY737SK5W5BZNPXEYJFAV6WDUI/action/storage_attestation","attest_author":"https://pith.science/pith/ZY737SK5W5BZNPXEYJFAV6WDUI/action/author_attestation","sign_citation":"https://pith.science/pith/ZY737SK5W5BZNPXEYJFAV6WDUI/action/citation_signature","submit_replication":"https://pith.science/pith/ZY737SK5W5BZNPXEYJFAV6WDUI/action/replication_record"}},"created_at":"2026-05-18T01:11:52.678760+00:00","updated_at":"2026-05-18T01:11:52.678760+00:00"}