In the analysis of various load-balancing schemes presented in Section 11.4.2, we assumed that the cost of transferring work is independent of the amount of work transferred. However, there are problems for which the work-transfer cost is a function of the amount of work transferred. Examples of such problems are found in tree-search applications for domains in which strong heuristics are available. For such applications, the size of the stack used to represent the search tree can vary significantly with the number of nodes in the search tree. Consider a case in which the size of the stack for representing a search space of w nodes varies as . Assume that the load-balancing scheme used is GRR. Analyze the performance of this scheme for a message passing architecture.