{"paper":{"title":"Solving Target Set Selection with Bounded Thresholds Faster than $2^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Danil Sagunov, Ivan Bliznets","submitted_at":"2018-07-27T18:37:43Z","abstract_excerpt":"In this paper we consider the Target Set Selection problem. The problem naturally arises in many fields like economy, sociology, medicine. In the Target Set Selection problem one is given a graph $G$ with a function $\\operatorname{thr}: V(G) \\to \\mathbb{N} \\cup \\{0\\}$ and integers $k, \\ell$. The goal of the problem is to activate at most $k$ vertices initially so that at the end of the activation process there is at least $\\ell$ activated vertices. The activation process occurs in the following way: (i) once activated, a vertex stays activated forever; (ii) vertex $v$ becomes activated if at l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10789","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"}