{"paper":{"title":"Constant-Time Algorithms for Sparsity Matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Hiro Ito, Shin-ichi Tanigawa, Yuichi Yoshida","submitted_at":"2011-03-14T03:51:27Z","abstract_excerpt":"A graph $G=(V,E)$ is called $(k,\\ell)$-full if $G$ contains a subgraph $H=(V,F)$ of $k|V|-\\ell$ edges such that, for any non-empty $F' \\subseteq F$, $|F'| \\leq k|V(F')| - \\ell$ holds. Here, $V(F')$ denotes the set of vertices incident to $F'$. It is known that the family of edge sets of $(k,\\ell)$-full graphs forms a family of matroid, known as the sparsity matroid of $G$. In this paper, we give a constant-time approximation algorithm for the rank of the sparsity matroid of a degree-bounded undirected graph. This leads to a constant-time tester for $(k,\\ell)$-fullness in the bounded-degree mod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2581","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":""},"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"}