Finite Branching Processes and AND/OR Tree Evaluation

This paper studies tail bounds on supercritical branching processes with nite distributions of oospring. Given a nite supercritical branching process fZ n g 1 0 , we derive upper bounds, decaying exponentially fast as c increases, on the right-tail probability PrZ n > cE(Z n)]. We obtain a similar upper bound on the left-tail probability PrrZ n < E(Zn) c ] under the assumption that each individual generates at least two oospring. As an application, we observe that the evaluation of an AND/OR tree by a canonical algorithm in certain probabilistic models can be viewed as a two-type supercritical nite branching process, and show that the execution time of this algorithm is likely to concentrate around its expectation.