{"paper":{"title":"Extended Formulations for Sparsity Matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.OC"],"primary_cat":"math.CO","authors_text":"Naoki Katoh, Naoyuki Kamiyama, Satoru Iwata, Shuji Kijima, Yoshio Okamoto","submitted_at":"2014-03-28T03:03:40Z","abstract_excerpt":"We show the existence of a polynomial-size extended formulation for the base polytope of a $(k,\\ell)$-sparsity matroid. For an undirected graph $G=(V,E)$, the size of the formulation is $O(|V||E|)$ when $k \\geq \\ell$ and $O(|V|^2 |E|)$ when $k \\leq \\ell$. To this end, we employ the technique developed by Faenza et al. recently that uses a randomized communication protocol."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7272","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"}