{"paper":{"title":"Betweenness Parameterized Above Tight Lower Bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Anders Yeo, Eun Jung Kim, Gregory Gutin, Matthias Mnich","submitted_at":"2009-07-30T21:26:12Z","abstract_excerpt":"We study ordinal embedding relaxations in the realm of parameterized complexity. We prove the existence of a quadratic kernel for the {\\sc Betweenness} problem parameterized above its tight lower bound, which is stated as follows. For a set $V$ of variables and set $\\mathcal C$ of constraints \"$v_i$ \\mbox{is between} $v_j$ \\mbox{and} $v_k$\", decide whether there is a bijection from $V$ to the set $\\{1,\\ldots,|V|\\}$ satisfying at least $|\\mathcal C|/3 + \\kappa$ of the constraints in $\\mathcal C$. Our result solves an open problem attributed to Benny Chor in Niedermeier's monograph \"Invitation t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.5427","kind":"arxiv","version":3},"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"}