{"paper":{"title":"Quasi-Polynomial Algorithms for Submodular Tree Orienteering and Other Directed Network Design Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Rohan Ghuge, Viswanath Nagarajan","submitted_at":"2018-12-05T01:07:31Z","abstract_excerpt":"We consider the following general network design problem on directed graphs. The input is an asymmetric metric $(V,c)$, root $r^{*}\\in V$, monotone submodular function $f:2^V\\rightarrow \\mathbb{R}_+$ and budget $B$. The goal is to find an $r^{*}$-rooted arborescence $T$ of cost at most $B$ that maximizes $f(T)$. Our main result is a simple quasi-polynomial time $O(\\frac{\\log k}{\\log\\log k})$-approximation algorithm for this problem, where $k\\le |V|$ is the number of vertices in an optimal solution. To the best of our knowledge, this is the first non-trivial approximation ratio for this problem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01768","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"}