A Linear-Time Algorithm for Constructing an Optimal Node-Search Strategy of a Tree
Ellis et al., proposed algorithms (in terms of vertex separation) to compute the node-search number of an n-vertex tree T in O(n) time and to construct an optimal node-search strategy of T in O(n log n) time. An open problem is whether the latter can also be done in linear time. In this paper, we solve this open problem by exploring fundamental graph theoretical properties.
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