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Given a vertex-weighted undirected graph\u00a0<jats:italic>G<\/jats:italic>, its objective is to find a maximum-weight induced subtree\u00a0<jats:italic>T<\/jats:italic> whose open neighborhood has size at most\u00a0<jats:italic>k<\/jats:italic>. We present a fixed-parameter tractable algorithm that solves the problem in time <jats:inline-formula><jats:tex-math>$$2^{\\mathcal {O} (k \\log k)}\\cdot n^{\\mathcal {O} (1)}$$<\/jats:tex-math><\/jats:inline-formula>, improving on a double-exponential running time from earlier work by Golovach, Heggernes, Lima, and Montealegre. Starting from a single vertex, our algorithm grows a <jats:italic>k<\/jats:italic>-secluded tree by branching on vertices in the open neighborhood of the current tree\u00a0<jats:italic>T<\/jats:italic>. To bound the branching depth, we prove a structural result that can be used to identify a vertex that belongs to the neighborhood of any <jats:italic>k<\/jats:italic>-secluded supertree\u00a0<jats:inline-formula><jats:tex-math>$$T' \\supseteq T$$<\/jats:tex-math><\/jats:inline-formula> once the open neighborhood of\u00a0<jats:italic>T<\/jats:italic> becomes sufficiently large. We extend the algorithm to enumerate compact descriptions of all maximum-weight <jats:italic>k<\/jats:italic>-secluded trees, which allows us to count the number of such trees containing a specified vertex in the same running time.<\/jats:p>","DOI":"10.1007\/978-3-031-15914-5_13","type":"book-chapter","created":{"date-parts":[[2022,9,30]],"date-time":"2022-09-30T11:14:22Z","timestamp":1664536462000},"page":"173-186","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Finding k-Secluded Trees Faster"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2767-8140","authenticated-orcid":false,"given":"Huib","family":"Donkers","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8204-1268","authenticated-orcid":false,"given":"Bart M. 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