  We study fair allocation of indivisible goods among additive agents with
feasibility constraints. In these settings, every agent is restricted to get a
bundle among a specified set of feasible bundles. Such scenarios have been of
great interest to the AI community due to their applicability to real-world
problems. Following some impossibility results, we restrict attention to
matroid feasibility constraints that capture natural scenarios, such as the
allocation of shifts to medical doctors, and the allocation of conference
papers to referees.
  We focus on the common fairness notion of envy-freeness up to one good (EF1).
Previous algorithms for finding EF1 allocations are either restricted to agents
with identical feasibility constraints, or allow free disposal of items. An
open problem is the existence of EF1 complete allocations among heterogeneous
agents, where the heterogeneity is both in the agents' feasibility constraints
and in their valuations. In this work, we make progress on this problem by
providing positive and negative results for different matroid and valuation
types. Among other results, we devise polynomial-time algorithms for finding
EF1 allocations in the following settings: (i) $n$ agents with heterogeneous
partition matroids and heterogeneous binary valuations, (ii) 2 agents with
heterogeneous partition matroids and heterogeneous additive valuations, and
(iii) at most 3 agents with heterogeneous binary valuations and identical
base-orderable matroid constraints.
