{"paper":{"title":"On uncrossing games for skew-supermodular functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hiroshi Hirai","submitted_at":"2015-09-29T03:03:26Z","abstract_excerpt":"In this note, we consider the uncrossing game for a skew-supermodular function $f$, which is a two-player game with players, Red and Blue, and abstracts the uncrossing procedure in the cut-covering linear program associated with $f$. Extending the earlier results by Karzanov for $\\{0,1\\}$-valued skew-supermodular functions, we present an improved polynomial time strategy for Red to win, and give a strongly polynomial time uncrossing procedure for dual solutions of the cut-covering LP as its consequence. We also mention its implication on the optimality of laminar solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08575","kind":"arxiv","version":2},"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"}