{"paper":{"title":"Node Labeling in Line Diagrams of Ordered Sets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Gerd Stumme, Marcel N\\\"ohre","submitted_at":"2026-07-25T16:37:21Z","abstract_excerpt":"We propose a flexible, two-phase algorithm for labeling line diagrams of ordered sets, in which the nodes of direct neighbors in the order relation are connected by a straight, upward-pointing line. In contrast to the labeling of diagrams of arbitrary graphs, we benefit from the fact that all edges in line diagrams of ordered sets are more or less vertical. In this paper, we study the placement of all labels such that they do not intersect with any nodes, lines, or other labels while minimizing the distances between the nodes and their labels.\n  Our approach starts by filtering the fixed-posit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23283","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.23283/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}