Three New Complexity Results for Resource Allocation Problems
  We prove the following results for task allocation of indivisible resources:   - The problem of finding a leximin-maximal resource allocation is in P if the agents have max-utility functions and atomic demands.   - Deciding whether a resource allocation is Pareto-optimal is coNP-complete for agents with (1-)additive utility functions.   - Deciding whether there exists a Pareto-optimal and envy-free resource allocation is Sigma_2^p-complete for agents with (1-)additive utility functions. 
Bart de Keijzer