{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5MVS746R7CCZEY6UP5REOJVN3R","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d03620da4e39b2fb7e3f9c9ac79a4cdcd38d44aa59db2a70bf6917be73ecb30d","cross_cats_sorted":["cs.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-11-28T21:51:40Z","title_canon_sha256":"c110949dc9b92850ee5392fa294f002180620c6261a96980875cf2096ada1eb3"},"schema_version":"1.0","source":{"id":"1412.0036","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0036","created_at":"2026-05-18T02:18:58Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0036v2","created_at":"2026-05-18T02:18:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0036","created_at":"2026-05-18T02:18:58Z"},{"alias_kind":"pith_short_12","alias_value":"5MVS746R7CCZ","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5MVS746R7CCZEY6U","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5MVS746R","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:0393a02094874d7e61e41abd1e3930ee934714d06ea01cdc898cbdf63eef8697","target":"graph","created_at":"2026-05-18T02:18:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The maximum volume $j$-simplex problem asks to compute the $j$-dimensional simplex of maximum volume inside the convex hull of a given set of $n$ points in $\\mathbb{Q}^d$. We give a deterministic approximation algorithm for this problem which achieves an approximation ratio of $e^{j/2 + o(j)}$. The problem is known to be $\\mathrm{NP}$-hard to approximate within a factor of $c^{j}$ for some constant $c > 1$. Our algorithm also gives a factor $e^{j + o(j)}$ approximation for the problem of finding the principal $j\\times j$ submatrix of a rank $d$ positive semidefinite matrix with the largest det","authors_text":"Aleksandar Nikolov","cross_cats":["cs.DS","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-11-28T21:51:40Z","title":"Randomized Rounding for the Largest Simplex Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0036","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:df4c58e7edecb63aa506bd65ed03298a3b2d9fdfa38ac4dd9046527c48b46847","target":"record","created_at":"2026-05-18T02:18:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d03620da4e39b2fb7e3f9c9ac79a4cdcd38d44aa59db2a70bf6917be73ecb30d","cross_cats_sorted":["cs.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2014-11-28T21:51:40Z","title_canon_sha256":"c110949dc9b92850ee5392fa294f002180620c6261a96980875cf2096ada1eb3"},"schema_version":"1.0","source":{"id":"1412.0036","kind":"arxiv","version":2}},"canonical_sha256":"eb2b2ff3d1f8859263d47f624726addc6fd4bf360981003f46314c80b9b8fb5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb2b2ff3d1f8859263d47f624726addc6fd4bf360981003f46314c80b9b8fb5c","first_computed_at":"2026-05-18T02:18:58.296421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:58.296421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bbKI4anSBAlVSM4hZ1kkrhY81b/CM36QjW/pzOyI97DItqBFGSGoCQiDMI7GOQozmtJcbvc1afW6sDR8mObwCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:58.297157Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.0036","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df4c58e7edecb63aa506bd65ed03298a3b2d9fdfa38ac4dd9046527c48b46847","sha256:0393a02094874d7e61e41abd1e3930ee934714d06ea01cdc898cbdf63eef8697"],"state_sha256":"abde20a14455f717ecd0781b23a6b615caa49cacb676607919d24522330061e5"}