{"paper":{"title":"Discrete Convexity in Joint Winner Property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Kazuo Murota, Stanislav Zivny, Yuni Iwamasa","submitted_at":"2017-01-26T10:40:44Z","abstract_excerpt":"In this paper, we reveal a relation between joint winner property (JWP) in the field of valued constraint satisfaction problems (VCSPs) and M${}^\\natural$-convexity in the field of discrete convex analysis (DCA). We introduce the M${}^\\natural$-convex completion problem, and show that a function $f$ satisfying the JWP is Z-free if and only if a certain function $\\overline{f}$ associated with $f$ is M${}^\\natural$-convex completable. This means that if a function is Z-free, then the function can be minimized in polynomial time via M${}^\\natural$-convex intersection algorithms. Furthermore we pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07645","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"}