{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:N2Z3PUV774WBA5T25P37JUSNBT","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":"62602683c70064415a3a3a331442a8b95c8125c80f9e67f928f712e09726e6c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-06-18T12:08:41Z","title_canon_sha256":"594ce90c21b68c9873947450541d2f0e43ef13cc145d36fc0b814e975ac24fb5"},"schema_version":"1.0","source":{"id":"1806.06617","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06617","created_at":"2026-05-18T00:08:30Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06617v2","created_at":"2026-05-18T00:08:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06617","created_at":"2026-05-18T00:08:30Z"},{"alias_kind":"pith_short_12","alias_value":"N2Z3PUV774WB","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"N2Z3PUV774WBA5T2","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"N2Z3PUV7","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:baf806d6a196f7ab022b8993b16a7868bdbcc8c9d6ea2fd41f19533645d590aa","target":"graph","created_at":"2026-05-18T00:08:30Z","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 consider the coordinate assignment phase of the well known Sugiyama framework for drawing directed graphs in a hierarchical style. The extensive literature in this area has given comparatively little attention to a prescribed width of the drawing. We present a minimum cost flow formulation that supports prescribed width and optionally other criteria like lower and upper bounds on the distance of neighbouring nodes in a layer or enforced vertical edges segments. In our experiments we demonstrate that our approach can compete with state-of-the-art algorithms.","authors_text":"Christiane Spisla, Michael J\\\"unger, Petra Mutzel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-06-18T12:08:41Z","title":"A Flow Formulation for Horizontal Coordinate Assignment with Prescribed Width"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06617","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":"sha256:84d81406e92ad482c7a17b1fd39358288aacb058c42f757b5fd518b2b0c8ab29","target":"record","created_at":"2026-05-18T00:08:30Z","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":"62602683c70064415a3a3a331442a8b95c8125c80f9e67f928f712e09726e6c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-06-18T12:08:41Z","title_canon_sha256":"594ce90c21b68c9873947450541d2f0e43ef13cc145d36fc0b814e975ac24fb5"},"schema_version":"1.0","source":{"id":"1806.06617","kind":"arxiv","version":2}},"canonical_sha256":"6eb3b7d2bfff2c10767aebf7f4d24d0cec9abcf29a33e8da810006c3fa90ce1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6eb3b7d2bfff2c10767aebf7f4d24d0cec9abcf29a33e8da810006c3fa90ce1d","first_computed_at":"2026-05-18T00:08:30.886714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:30.886714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2oL1mFHJ3lcjQn3aTafyjOKCWHrK4du6iv2qfgFbf7Ey/1/aSK6WwfWZy6CttZIdS5hSXjdUyGm7eU/B8ho7Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:30.887196Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.06617","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84d81406e92ad482c7a17b1fd39358288aacb058c42f757b5fd518b2b0c8ab29","sha256:baf806d6a196f7ab022b8993b16a7868bdbcc8c9d6ea2fd41f19533645d590aa"],"state_sha256":"64376c2dc2c80878996ab1472ceee4c94f8f6bcacb8bedc7beb0b67405fb5f05"}