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.