On the tree search problem with non-uniform costs

We improve upon the above results both from the algorithmic and the computational complexity point of view: We provide a novel algorithm that provides an O(log⁡nlog⁡log⁡n)-approximation of the cost of the optimal strategy. In addition, we show that finding an optimal strategy is NP-hard even when the input tree is a spider of diameter 6, i.e., at most one vertex has degree larger than 2.