{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SMBJ3PCVSG3QHYWOLD3EKYBCDE","short_pith_number":"pith:SMBJ3PCV","canonical_record":{"source":{"id":"1604.07049","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-24T16:40:41Z","cross_cats_sorted":["cs.DM","cs.DS","math.CO"],"title_canon_sha256":"221a892518c6d541897512133b8727114f33066836d488d118d53576548ba8e9","abstract_canon_sha256":"84137c6dcfbbc30de8b16049f0203c8b4aac0f01518aabffb038d8c1c1694577"},"schema_version":"1.0"},"canonical_sha256":"93029dbc5591b703e2ce58f6456022192774ef20fb7315c4f8ac03db8704106a","source":{"kind":"arxiv","id":"1604.07049","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.07049","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"arxiv_version","alias_value":"1604.07049v1","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07049","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"pith_short_12","alias_value":"SMBJ3PCVSG3Q","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SMBJ3PCVSG3QHYWO","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SMBJ3PCV","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SMBJ3PCVSG3QHYWOLD3EKYBCDE","target":"record","payload":{"canonical_record":{"source":{"id":"1604.07049","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-24T16:40:41Z","cross_cats_sorted":["cs.DM","cs.DS","math.CO"],"title_canon_sha256":"221a892518c6d541897512133b8727114f33066836d488d118d53576548ba8e9","abstract_canon_sha256":"84137c6dcfbbc30de8b16049f0203c8b4aac0f01518aabffb038d8c1c1694577"},"schema_version":"1.0"},"canonical_sha256":"93029dbc5591b703e2ce58f6456022192774ef20fb7315c4f8ac03db8704106a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:23.185181Z","signature_b64":"bzgm7Hv2D9nEeznIMfaqb++k5YG5nehWrd908ObfnTeD0KEugN8chJWQJtaVqufAo/qH4kbG4JKOrrbhQuFtDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93029dbc5591b703e2ce58f6456022192774ef20fb7315c4f8ac03db8704106a","last_reissued_at":"2026-05-18T01:16:23.184643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:23.184643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.07049","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yrMpX9rt/E0U+rAMzBVEJZB5RXD3dH2Hdh8B+h61ACBB10aM6mWNlfwik4+HYc+2ObLBb4Kmfnj4SCQs4MIvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T04:27:31.759618Z"},"content_sha256":"6ff4eafa1f029255c8714dba0db1c50f3575c688e0271647ede6cb765e1786c2","schema_version":"1.0","event_id":"sha256:6ff4eafa1f029255c8714dba0db1c50f3575c688e0271647ede6cb765e1786c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SMBJ3PCVSG3QHYWOLD3EKYBCDE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast Approximation Algorithms for the Generalized Survivable Network Design Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS","math.CO"],"primary_cat":"math.OC","authors_text":"Andreas Emil Feldmann, Jochen K\\\"onemann, Kanstantsin Pashkovich, Laura Sanit\\`a","submitted_at":"2016-04-24T16:40:41Z","abstract_excerpt":"In a standard $f$-connectivity network design problem, we are given an undirected graph $G=(V,E)$, a cut-requirement function $f:2^V \\rightarrow {\\mathbb{N}}$, and non-negative costs $c(e)$ for all $e \\in E$. We are then asked to find a minimum-cost vector $x \\in {\\mathbb{N}}^E$ such that $x(\\delta(S)) \\geq f(S)$ for all $S \\subseteq V$. We focus on the class of such problems where $f$ is a proper function. This encodes many well-studied NP-hard problems such as the generalized survivable network design problem.\n  In this paper we present the first strongly polynomial time FPTAS for solving th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07049","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C7dYSdDA39D6I9YWvBtUFvueNSTLGXZeKjHYxzSFCUF5rceVNMa8EwGeHzF05ewjBnT/3LbbJpMHl9mh5fMtBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T04:27:31.760296Z"},"content_sha256":"d292c6cbed8ced17dd031521510a085278877868817620838b8a77fb5436c217","schema_version":"1.0","event_id":"sha256:d292c6cbed8ced17dd031521510a085278877868817620838b8a77fb5436c217"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SMBJ3PCVSG3QHYWOLD3EKYBCDE/bundle.json","state_url":"https://pith.science/pith/SMBJ3PCVSG3QHYWOLD3EKYBCDE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SMBJ3PCVSG3QHYWOLD3EKYBCDE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-24T04:27:31Z","links":{"resolver":"https://pith.science/pith/SMBJ3PCVSG3QHYWOLD3EKYBCDE","bundle":"https://pith.science/pith/SMBJ3PCVSG3QHYWOLD3EKYBCDE/bundle.json","state":"https://pith.science/pith/SMBJ3PCVSG3QHYWOLD3EKYBCDE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SMBJ3PCVSG3QHYWOLD3EKYBCDE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SMBJ3PCVSG3QHYWOLD3EKYBCDE","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":"84137c6dcfbbc30de8b16049f0203c8b4aac0f01518aabffb038d8c1c1694577","cross_cats_sorted":["cs.DM","cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-24T16:40:41Z","title_canon_sha256":"221a892518c6d541897512133b8727114f33066836d488d118d53576548ba8e9"},"schema_version":"1.0","source":{"id":"1604.07049","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.07049","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"arxiv_version","alias_value":"1604.07049v1","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07049","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"pith_short_12","alias_value":"SMBJ3PCVSG3Q","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SMBJ3PCVSG3QHYWO","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SMBJ3PCV","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:d292c6cbed8ced17dd031521510a085278877868817620838b8a77fb5436c217","target":"graph","created_at":"2026-05-18T01:16:23Z","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":"In a standard $f$-connectivity network design problem, we are given an undirected graph $G=(V,E)$, a cut-requirement function $f:2^V \\rightarrow {\\mathbb{N}}$, and non-negative costs $c(e)$ for all $e \\in E$. We are then asked to find a minimum-cost vector $x \\in {\\mathbb{N}}^E$ such that $x(\\delta(S)) \\geq f(S)$ for all $S \\subseteq V$. We focus on the class of such problems where $f$ is a proper function. This encodes many well-studied NP-hard problems such as the generalized survivable network design problem.\n  In this paper we present the first strongly polynomial time FPTAS for solving th","authors_text":"Andreas Emil Feldmann, Jochen K\\\"onemann, Kanstantsin Pashkovich, Laura Sanit\\`a","cross_cats":["cs.DM","cs.DS","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-24T16:40:41Z","title":"Fast Approximation Algorithms for the Generalized Survivable Network Design Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07049","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":"sha256:6ff4eafa1f029255c8714dba0db1c50f3575c688e0271647ede6cb765e1786c2","target":"record","created_at":"2026-05-18T01:16:23Z","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":"84137c6dcfbbc30de8b16049f0203c8b4aac0f01518aabffb038d8c1c1694577","cross_cats_sorted":["cs.DM","cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-04-24T16:40:41Z","title_canon_sha256":"221a892518c6d541897512133b8727114f33066836d488d118d53576548ba8e9"},"schema_version":"1.0","source":{"id":"1604.07049","kind":"arxiv","version":1}},"canonical_sha256":"93029dbc5591b703e2ce58f6456022192774ef20fb7315c4f8ac03db8704106a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93029dbc5591b703e2ce58f6456022192774ef20fb7315c4f8ac03db8704106a","first_computed_at":"2026-05-18T01:16:23.184643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:23.184643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bzgm7Hv2D9nEeznIMfaqb++k5YG5nehWrd908ObfnTeD0KEugN8chJWQJtaVqufAo/qH4kbG4JKOrrbhQuFtDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:23.185181Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.07049","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ff4eafa1f029255c8714dba0db1c50f3575c688e0271647ede6cb765e1786c2","sha256:d292c6cbed8ced17dd031521510a085278877868817620838b8a77fb5436c217"],"state_sha256":"2d0aca9c79784e5ccb92efa352f78f4df384e2a3991b8a3ef712ed2d0af5f2b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d7gfjDWvSsdoMMM0FRvzG4YyfpTY5sQXltH0HpEM04NnOx6eNKN9vi96FVZ8ASIZMeYSO9j/V5OSklasnhe/Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T04:27:31.763965Z","bundle_sha256":"07e5798ac8fcc0a135c4ad9ef43afe5a36138bfa3db4e66810edaa7a9802f154"}}