{"paper":{"title":"Algorithms for Cut Problems on Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Binhai Zhu, Boting Yang, Fenghui Zhang, Ge Xia, Guohui Lin, Iyad Kanj, Jinhui Xu, Peng Zhang, Tian Liu, Weitian Tong","submitted_at":"2013-04-12T14:57:47Z","abstract_excerpt":"We study the {\\sc multicut on trees} and the {\\sc generalized multiway Cut on trees} problems. For the {\\sc multicut on trees} problem, we present a parameterized algorithm that runs in time $O^{*}(\\rho^k)$, where $\\rho = \\sqrt{\\sqrt{2} + 1} \\approx 1.555$ is the positive root of the polynomial $x^4-2x^2-1$. This improves the current-best algorithm of Chen et al. that runs in time $O^{*}(1.619^k)$. For the {\\sc generalized multiway cut on trees} problem, we show that this problem is solvable in polynomial time if the number of terminal sets is fixed; this answers an open question posed in a re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3653","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"}