Finding k-secluded trees faster

We revisit the k-Secluded Tree problem. Given a vertex-weighted undirected graph G, its objective is to find maximum-weight induced subtree T whose open neighborhood has size at most k. present fixed-parameter tractable algorithm that solves problem in time 2O(klog⁡k)⋅nO(1), improving on double-exponential running from earlier work by Golovach, Heggernes, Lima, and Montealegre. Starting single vertex, our grows k-secluded tree branching vertices of current T. To bound depth, we prove structural result can be used identify vertex belongs any supertree T′⊇T once becomes sufficiently large. extend enumerate compact descriptions all trees, which allows us count them as well.