Depth-Workload Tradeoffs for Workforce Organization

Abstract

We introduce and consider the problem of effectively organizing a population of workers of varying abilities. We assume that arriving tasks for the workforce are homogeneous, and that each is characterized by an unknown and one- dimensional difficulty value x ∈ [0, 1]. Each worker i is characterized by their ability w_i ∈ [0, 1], and can solve the task if and only if x ≤ w_i. If a worker is unable to solve a given task it must be forwarded to a worker of greater ability. For a given set of worker abilities W and a distribution P over task difficulty, we are interested in the problem of designing efficient forwarding structures for W and P. We give efficient algorithms and structures that simultaneously (approximately) minimize both the maximum workload of any worker, and the number of workers that need to attempt a task. We identify broad conditions under which workloads diminish rapidly with the workforce size, yet only a constant number of workers attempt each task.