  We consider a multi-agent resource allocation setting that models the
assignment of papers to reviewers. A recurring issue in allocation problems is
the compatibility of welfare/efficiency and fairness. Given an oracle to find a
welfare-achieving allocation, we embed such an oracle into a flexible algorithm
called the Constrained Round Robin (CRR) algorithm, that achieves the required
welfare level. Our algorithm also allows the system designer to lower the
welfare requirements in order to achieve a higher degree of fairness. If the
welfare requirement is lowered enough, a strengthening of envy-freeness up to
one item is guaranteed. Hence, our algorithm can be viewed as a computationally
efficient way to interpolate between welfare and approximate envy-freeness in
allocation problems.
