{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IHGZVLO4QPEAOMHVY6XG2O6N5E","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":"7df79f91c883dae9a56fc56f6c192a6173b1418cef6a1a8a83c65311670f3d70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-16T14:12:07Z","title_canon_sha256":"1d5c7beef69d0c66cbdc1cad6355111006071148a6bee272b6cf0a9bfd355380"},"schema_version":"1.0","source":{"id":"1612.05474","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05474","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05474v1","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05474","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"pith_short_12","alias_value":"IHGZVLO4QPEA","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IHGZVLO4QPEAOMHV","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IHGZVLO4","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:e064418441eabe6d799a5d8f4d35e566e455dc3c2d940dc29d933ebc9f5ad2a2","target":"graph","created_at":"2026-05-18T00:54:51Z","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":"We generalize the fractional packing framework of Garg and Koenemann to the case of linear fractional packing problems over polyhedral cones. More precisely, we provide approximation algorithms for problems of the form $\\max\\{c^T x : Ax \\leq b, x \\in C \\}$, where the matrix $A$ contains no negative entries and $C$ is a cone that is generated by a finite set $S$ of non-negative vectors. While the cone is allowed to require an exponential-sized representation, we assume that we can access it via one of three types of oracles. For each of these oracles, we present positive results for the approxi","authors_text":"Michael Holzhauser, Sven O. Krumke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-16T14:12:07Z","title":"A Generalized Approximation Framework for Fractional Network Flow and Packing Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05474","kind":"arxiv","version":1},"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":"sha256:3ce1fd4a37ce81ea09ecdbb0296bef474d47a1fdeb381f2b53a4eea20131abed","target":"record","created_at":"2026-05-18T00:54:51Z","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":"7df79f91c883dae9a56fc56f6c192a6173b1418cef6a1a8a83c65311670f3d70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-16T14:12:07Z","title_canon_sha256":"1d5c7beef69d0c66cbdc1cad6355111006071148a6bee272b6cf0a9bfd355380"},"schema_version":"1.0","source":{"id":"1612.05474","kind":"arxiv","version":1}},"canonical_sha256":"41cd9aaddc83c80730f5c7ae6d3bcde9163acdbc6411557e4d2d81ef382b366e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41cd9aaddc83c80730f5c7ae6d3bcde9163acdbc6411557e4d2d81ef382b366e","first_computed_at":"2026-05-18T00:54:51.704448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:51.704448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D+FiMUuCACXHoecVzmvUtvjSGs4VHZMRzmtLMuVpLtPvmpO14tPJDI3F3pUD2O8aSEkA+0v+fOH1RNErUXqjDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:51.705090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.05474","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ce1fd4a37ce81ea09ecdbb0296bef474d47a1fdeb381f2b53a4eea20131abed","sha256:e064418441eabe6d799a5d8f4d35e566e455dc3c2d940dc29d933ebc9f5ad2a2"],"state_sha256":"8288194cf11ffaa8c4c9d1a01ab7e7f51f6d7d7ff17ff56304639957f421f3fa"}