Generalization of Binary Search: Searching in Trees and Forest-Like Partial Orders

We extend the binary search technique to searching in trees. We consider two models of queries: questions about vertices and questions about edges. We present a general approach to this sort of problem, and apply it to both cases, achieving algorithms constructing optimal decision trees. In the edge query model the problem is identical to the problem of searching in a special class of tree-like posets stated by Ben-Asher, Farchi and Newman [1]. Our upper bound on computation time, O(n^3 ), improves the previous best known O(n^4 log^3 n). In the vertex query model we show how to compute an optimal strategy much faster, in O(n) steps. We also present an almost optimal approximation algorithmfor another class of tree-like (and forest-like) partial orders.