{"paper":{"title":"Covering vertices by sequential stars","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"An Zhang, Guohui Lin, Jiaxuan Ma, Mengyuan Hu, Wei Ding, Yong Chen, Yue Sun, Zhikai Chen","submitted_at":"2026-05-23T19:31:47Z","abstract_excerpt":"We study the problem of covering the maximum number of vertices in a graph by a collection of vertex-disjoint stars, each with a number of satellites in a given interval $[k, \\ell]$, where $1 \\le k < \\ell$ and $\\ell$ can be infinity. This is referred to as sequential {\\sc $[k, \\ell]$-Star Packing} problem. It is solvable in polynomial time when $k = 1$, but becomes strongly NP-hard when $k \\ge 2$. In this paper, we propose either the first or an improved approximation algorithm for the following four sequential settings: 1) a $\\frac {k+1}2$-approximation algorithm when $k \\ge 3$ and $\\ell = \\i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24711","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/2605.24711/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"}