Two Algorithms for Additive and Fair Division of Mixed Manna

We consider a fair division model in which agents have positive, zero and negative utilities for items. For this model, we analyse one existing fairness property - EFX - and three new and related properties - EFX0, EFX3 and EF13 - in combination with Pareto-optimality. With general utilities, we give a modified version of an existing algorithm for computing an EF13 allocation. With -α/0/α utilities, this algorithm returns an EFX3 and PO allocation. With absolute identical utilities, we give a new algorithm for an EFX and PO allocation. With -α/0/β utilities, this algorithm also returns such an allocation. We report some new impossibility results as well.