{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SEPTWRD2N3OSFRVETIJW6MDVT5","short_pith_number":"pith:SEPTWRD2","canonical_record":{"source":{"id":"2605.13402","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2026-05-13T11:57:35Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"9a100120b5d9f29eaeb9d42f5fb38e41f00b3b219b4b3910a995deae3864c268","abstract_canon_sha256":"54db0d31b1f55f59b9df307be7c8d02f54d28d13ec662aa73933e849fde5fae8"},"schema_version":"1.0"},"canonical_sha256":"911f3b447a6edd22c6a49a136f30759f608d2f8b72123be0ada37eb46bfdacae","source":{"kind":"arxiv","id":"2605.13402","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13402","created_at":"2026-05-18T02:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13402v1","created_at":"2026-05-18T02:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13402","created_at":"2026-05-18T02:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"SEPTWRD2N3OS","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"SEPTWRD2N3OSFRVE","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"SEPTWRD2","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SEPTWRD2N3OSFRVETIJW6MDVT5","target":"record","payload":{"canonical_record":{"source":{"id":"2605.13402","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2026-05-13T11:57:35Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"9a100120b5d9f29eaeb9d42f5fb38e41f00b3b219b4b3910a995deae3864c268","abstract_canon_sha256":"54db0d31b1f55f59b9df307be7c8d02f54d28d13ec662aa73933e849fde5fae8"},"schema_version":"1.0"},"canonical_sha256":"911f3b447a6edd22c6a49a136f30759f608d2f8b72123be0ada37eb46bfdacae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:47.582015Z","signature_b64":"RT5tpUXxYY7r7oRyt1Uvzs4Tb82O/5llQwHjR/fa+60oZGEW5ddRbQjz26yjcJJXssb9QoEAv+g5W+i0wH8NCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"911f3b447a6edd22c6a49a136f30759f608d2f8b72123be0ada37eb46bfdacae","last_reissued_at":"2026-05-18T02:44:47.581611Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:47.581611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.13402","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":"2026-05-18T02:44:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BkzlFByxvgxZ9sFLPKiNGZCetAa9i1+O1HYOCbU1nzSDsEfiATHHyXEpoQocbFC0X3mnDVNrvaXsJu+dJtuMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T22:11:19.279439Z"},"content_sha256":"0e2f4cca691fe7366e2a93f78639834eb299d3a46be4fa55f40bd06275122e84","schema_version":"1.0","event_id":"sha256:0e2f4cca691fe7366e2a93f78639834eb299d3a46be4fa55f40bd06275122e84"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SEPTWRD2N3OSFRVETIJW6MDVT5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The fcBK algorithm computes minimum s-t cuts in O(m|C|) time using a compact graph representation for graphs with billions of vertices.","cross_cats":["cs.DS"],"primary_cat":"cs.CV","authors_text":"Anders Bjorholm Dahl, Christian M{\\o}ller Mikkelstrup, Inge Li G{\\o}rtz, Philip Bille, Vedrana Andersen Dahl","submitted_at":"2026-05-13T11:57:35Z","abstract_excerpt":"Computing a minimum $s$-$t$ cut in a graph is a solution to a wide range of computer vision problems, and is often done using the Boykov-Kolmogorov (BK) algorithm. In this paper, we revisit the BK algorithm from both a theoretical and practical point of view. We improve the analysis of the time complexity of the BK algorithm to $O(mn|C|)$ and propose a new algorithm, the fast and compact BK (fcBK) algorithm, with a time complexity of $O(m|C|)$, where $m$, $n$, and $|C|$ are the number of edges, number of vertices, and the capacity of the cut, respectively. We additionally propose a compact gra"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We propose a new algorithm, the fast and compact BK (fcBK) algorithm, with a time complexity of O(m|C|), where m and |C| are the number of edges and the capacity of the cut, respectively.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The compact graph representation preserves the correctness of the minimum-cut computation and incurs no hidden asymptotic overhead on the claimed time bound.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The fcBK algorithm computes minimum s-t cuts in O(m|C|) time and supports graphs with up to 10^9 vertices using a compact representation.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The fcBK algorithm computes minimum s-t cuts in O(m|C|) time using a compact graph representation for graphs with billions of vertices.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"902307208967bd106259c29c8594bfc6e98c55a205e343876e59e93462d52da6"},"source":{"id":"2605.13402","kind":"arxiv","version":1},"verdict":{"id":"0e891b51-fb6d-4859-b8a9-2b81dfc3b37f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:41:44.333762Z","strongest_claim":"We propose a new algorithm, the fast and compact BK (fcBK) algorithm, with a time complexity of O(m|C|), where m and |C| are the number of edges and the capacity of the cut, respectively.","one_line_summary":"The fcBK algorithm computes minimum s-t cuts in O(m|C|) time and supports graphs with up to 10^9 vertices using a compact representation.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The compact graph representation preserves the correctness of the minimum-cut computation and incurs no hidden asymptotic overhead on the claimed time bound.","pith_extraction_headline":"The fcBK algorithm computes minimum s-t cuts in O(m|C|) time using a compact graph representation for graphs with billions of vertices."},"references":{"count":60,"sample":[{"doi":"","year":2004,"title":"An experimental comparison of min- cut/max-flow algorithms for energy minimization in vision,","work_id":"be597a52-54bc-4572-93f7-9387eafaaae2","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2001,"title":"Interactive graph cuts for optimal boundary & region segmentation of objects in n-d images,","work_id":"05a58ed5-bdbb-4b66-bc56-b8ce7eed2032","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2005,"title":"Efficiently solving dynamic markov random fields using graph cuts,","work_id":"d5bea19f-b0ca-4015-a73f-f10fb2f202c8","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2006,"title":"Graph cuts and efficient n-d image segmentation,","work_id":"f04c6a05-9e51-46b9-8969-7da48b8f6071","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"Fast approximate energy minimization with label costs,","work_id":"e02cf547-53b2-46c9-8319-2618c33633a7","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":60,"snapshot_sha256":"2ae27956d09394e44fcd163371f258dafed2b2154f86733ccfe7eb74ad81645d","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":"0e891b51-fb6d-4859-b8a9-2b81dfc3b37f"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DSY4cGIAoEy29fzYlZoFQ6zJ+DIiHaUyft/MS2fJDFX7I+xhStkZarioZrFyt4EbaacixwIpR/ATFOGMIU7TDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T22:11:19.280429Z"},"content_sha256":"ea4d010c47d3b981373c9eab97d90a0aba205c8ae523ce8a757a7eb24f0a5818","schema_version":"1.0","event_id":"sha256:ea4d010c47d3b981373c9eab97d90a0aba205c8ae523ce8a757a7eb24f0a5818"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SEPTWRD2N3OSFRVETIJW6MDVT5/bundle.json","state_url":"https://pith.science/pith/SEPTWRD2N3OSFRVETIJW6MDVT5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SEPTWRD2N3OSFRVETIJW6MDVT5/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":"2026-05-22T22:11:19Z","links":{"resolver":"https://pith.science/pith/SEPTWRD2N3OSFRVETIJW6MDVT5","bundle":"https://pith.science/pith/SEPTWRD2N3OSFRVETIJW6MDVT5/bundle.json","state":"https://pith.science/pith/SEPTWRD2N3OSFRVETIJW6MDVT5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SEPTWRD2N3OSFRVETIJW6MDVT5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SEPTWRD2N3OSFRVETIJW6MDVT5","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":"54db0d31b1f55f59b9df307be7c8d02f54d28d13ec662aa73933e849fde5fae8","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2026-05-13T11:57:35Z","title_canon_sha256":"9a100120b5d9f29eaeb9d42f5fb38e41f00b3b219b4b3910a995deae3864c268"},"schema_version":"1.0","source":{"id":"2605.13402","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13402","created_at":"2026-05-18T02:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13402v1","created_at":"2026-05-18T02:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13402","created_at":"2026-05-18T02:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"SEPTWRD2N3OS","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"SEPTWRD2N3OSFRVE","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"SEPTWRD2","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:ea4d010c47d3b981373c9eab97d90a0aba205c8ae523ce8a757a7eb24f0a5818","target":"graph","created_at":"2026-05-18T02:44:47Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We propose a new algorithm, the fast and compact BK (fcBK) algorithm, with a time complexity of O(m|C|), where m and |C| are the number of edges and the capacity of the cut, respectively."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The compact graph representation preserves the correctness of the minimum-cut computation and incurs no hidden asymptotic overhead on the claimed time bound."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"The fcBK algorithm computes minimum s-t cuts in O(m|C|) time and supports graphs with up to 10^9 vertices using a compact representation."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The fcBK algorithm computes minimum s-t cuts in O(m|C|) time using a compact graph representation for graphs with billions of vertices."}],"snapshot_sha256":"902307208967bd106259c29c8594bfc6e98c55a205e343876e59e93462d52da6"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Computing a minimum $s$-$t$ cut in a graph is a solution to a wide range of computer vision problems, and is often done using the Boykov-Kolmogorov (BK) algorithm. In this paper, we revisit the BK algorithm from both a theoretical and practical point of view. We improve the analysis of the time complexity of the BK algorithm to $O(mn|C|)$ and propose a new algorithm, the fast and compact BK (fcBK) algorithm, with a time complexity of $O(m|C|)$, where $m$, $n$, and $|C|$ are the number of edges, number of vertices, and the capacity of the cut, respectively. We additionally propose a compact gra","authors_text":"Anders Bjorholm Dahl, Christian M{\\o}ller Mikkelstrup, Inge Li G{\\o}rtz, Philip Bille, Vedrana Andersen Dahl","cross_cats":["cs.DS"],"headline":"The fcBK algorithm computes minimum s-t cuts in O(m|C|) time using a compact graph representation for graphs with billions of vertices.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2026-05-13T11:57:35Z","title":"Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm"},"references":{"count":60,"internal_anchors":0,"resolved_work":60,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"An experimental comparison of min- cut/max-flow algorithms for energy minimization in vision,","work_id":"be597a52-54bc-4572-93f7-9387eafaaae2","year":2004},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Interactive graph cuts for optimal boundary & region segmentation of objects in n-d images,","work_id":"05a58ed5-bdbb-4b66-bc56-b8ce7eed2032","year":2001},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Efficiently solving dynamic markov random fields using graph cuts,","work_id":"d5bea19f-b0ca-4015-a73f-f10fb2f202c8","year":2005},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Graph cuts and efficient n-d image segmentation,","work_id":"f04c6a05-9e51-46b9-8969-7da48b8f6071","year":2006},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Fast approximate energy minimization with label costs,","work_id":"e02cf547-53b2-46c9-8319-2618c33633a7","year":2012}],"snapshot_sha256":"2ae27956d09394e44fcd163371f258dafed2b2154f86733ccfe7eb74ad81645d"},"source":{"id":"2605.13402","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T20:41:44.333762Z","id":"0e891b51-fb6d-4859-b8a9-2b81dfc3b37f","model_set":{"reader":"grok-4.3"},"one_line_summary":"The fcBK algorithm computes minimum s-t cuts in O(m|C|) time and supports graphs with up to 10^9 vertices using a compact representation.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The fcBK algorithm computes minimum s-t cuts in O(m|C|) time using a compact graph representation for graphs with billions of vertices.","strongest_claim":"We propose a new algorithm, the fast and compact BK (fcBK) algorithm, with a time complexity of O(m|C|), where m and |C| are the number of edges and the capacity of the cut, respectively.","weakest_assumption":"The compact graph representation preserves the correctness of the minimum-cut computation and incurs no hidden asymptotic overhead on the claimed time bound."}},"verdict_id":"0e891b51-fb6d-4859-b8a9-2b81dfc3b37f"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0e2f4cca691fe7366e2a93f78639834eb299d3a46be4fa55f40bd06275122e84","target":"record","created_at":"2026-05-18T02:44:47Z","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":"54db0d31b1f55f59b9df307be7c8d02f54d28d13ec662aa73933e849fde5fae8","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2026-05-13T11:57:35Z","title_canon_sha256":"9a100120b5d9f29eaeb9d42f5fb38e41f00b3b219b4b3910a995deae3864c268"},"schema_version":"1.0","source":{"id":"2605.13402","kind":"arxiv","version":1}},"canonical_sha256":"911f3b447a6edd22c6a49a136f30759f608d2f8b72123be0ada37eb46bfdacae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"911f3b447a6edd22c6a49a136f30759f608d2f8b72123be0ada37eb46bfdacae","first_computed_at":"2026-05-18T02:44:47.581611Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:47.581611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RT5tpUXxYY7r7oRyt1Uvzs4Tb82O/5llQwHjR/fa+60oZGEW5ddRbQjz26yjcJJXssb9QoEAv+g5W+i0wH8NCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:47.582015Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13402","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e2f4cca691fe7366e2a93f78639834eb299d3a46be4fa55f40bd06275122e84","sha256:ea4d010c47d3b981373c9eab97d90a0aba205c8ae523ce8a757a7eb24f0a5818"],"state_sha256":"d1aa7a09bc60fdb8a81198916a50609eba40556636c42f429f077afaf11780a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NRfXbTbBlUX/Tn1b+1IFRZBIo5g2DdJV59q38cTG8NnI3c3PC2nOzFZQcbbrd4q31jvbxQ1pTVnPHP4BUi8AAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T22:11:19.283849Z","bundle_sha256":"b7fafb3a4fbb1372e41f5e9add9c5e16a81e9d6298609e48bdfab6dedaab974a"}}