{"paper":{"title":"Approximation algorithms for non-sequential star packing problems","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"An Zhang, Guohui Lin, Mengyuan Hu, Mingyang Gong, Yong Chen","submitted_at":"2024-11-17T17:46:18Z","abstract_excerpt":"For a positive integer $k \\ge 1$, a $k$-star ($k^+$-star, $k^-$-star, respectively) is a connected graph containing a degree-$\\ell$ vertex and $\\ell$ degree-$1$ vertices, where $\\ell = k$ ($\\ell \\ge k$, $1 \\le \\ell \\le k$, respectively). The $k^+$-star packing problem is to cover as many vertices of an input graph $G$ as possible using vertex-disjoint $k^+$-stars in $G$; and given $k > t \\ge 1$, the $k^-/t$-star packing problem is to cover as many vertices of $G$ as possible using vertex-disjoint $k^-$-stars but no $t$-stars in $G$. Both problems are NP-hard for any fixed $k \\ge 2$. We present"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.11136","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/2411.11136/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"}