Consider a parallel formulation of best-first search of a graph that uses a hash function to distribute nodes to processors (Section 11.5). The performance of this scheme is influenced by two factors: the communication cost and the number of "good" nodes expanded (a "good" node is one that would also be expanded by the sequential algorithm). These two factors can be analyzed independently of each other. Assuming a completely random hash function (one in which each node has a probability of being hashed to a processor equal to 1/p), show that the expected number of nodes expanded by this parallel formulation differs from the optimal number by a constant factor (that is, independent of p). Assuming that the cost of communicating a node from one processor to another is O (1), derive the isoefficiency function of this scheme.