{"paper":{"title":"Breadth-First Search in Succinct Planar Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.DS","authors_text":"Johannes Meintrup","submitted_at":"2026-07-07T12:45:03Z","abstract_excerpt":"We present a succinct encoding of planar graphs that supports executing a breadth-first search directly on the encoding. The succinct encoding can be constructed in expected $O(n)$ time using $O(n)$ bits during construction; a compact variant can be constructed in deterministic $O(n)$ time using $O(n)$ bits. Once the encoding is constructed, a BFS from any start vertex can be computed in $O(n)$ time using $o(n)$ additional bits, including the space needed to represent the BFS tree. The resulting BFS tree $T$ remains available for standard tree operations, such as traversal, parent and child qu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06221","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/2607.06221/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"}