{"paper":{"title":"An $O^*(1.84^k)$ Parameterized Algorithm for the Multiterminal Cut Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jia-Hao Fan, Jianer Chen, Yixin Cao","submitted_at":"2017-11-17T04:26:10Z","abstract_excerpt":"We study the \\emph{multiterminal cut} problem, which, given an $n$-vertex graph whose edges are integer-weighted and a set of terminals, asks for a partition of the vertex set such that each terminal is in a distinct part, and the total weight of crossing edges is at most $k$. Our weapons shall be two classical results known for decades: \\emph{maximum volume minimum ($s,t$)-cuts} by [Ford and Fulkerson, \\emph{Flows in Networks}, 1962] and \\emph{isolating cuts} by [Dahlhaus et al., \\emph{SIAM J. Comp.} 23(4):864-894, 1994]. We sharpen these old weapons with the help of submodular functions, and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06397","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"}