Optimal search in trees - extended abstract+appendix

It is well known that the optimal solution for searching in a finite total order set is the binary search. In binary search we divide the set into two `halves', by querying the middle element, and continue the search on the suitable half. What is the equivalent of binary search, when the set P is partially ordered? A query in this case is to a point xεP, with two possible answers: `yes', indicates that the required element is `below' x, or `no' if the element is not bellow x. We show that the problem of computing an optimal strategy for search in Posets that are tree-like (or forests) is polynomial in the size of the tree, and requires at most O(n²log²n) steps. Optimal solutions of such search problems are often needed in program testing and debugging, where a given program is represented as a tree and a bug should be found using a minimal set of queries.