{"paper":{"title":"Structural parameterizations of Geodetic Set on directed (acyclic) graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Beaudou Laurent, Foucaud Florent, Lorieau Lucas, Tale Prafullkumar","submitted_at":"2026-06-24T22:11:45Z","abstract_excerpt":"In DIRECTED GEODETIC SET, we are given a (directed) graph and seek a small solution set $S \\subseteq V(G)$ such that every vertex lies on a shortest directed path between two vertices in $S$.\n  It is known that the problem is W[2]-hard when parameterized by the solution size $k$, even on directed acyclic graphs (DAGs).\n  Our first result is a kernel of size $2^{O(vcn)}$ for DIRECTED GEODETIC SET on general digraphs, where $vcn$ denotes the vertex cover number of the underlying (undirected) graph. This implies an algorithm running in time $2^{O(vcn^2)} \\cdot n^{O(1)}$. Furthermore, we prove tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26414","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/2606.26414/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"}