  We present fast, fair, flexible, and welfare efficient algorithms for
assigning reviewers to submitted conference papers. Our approaches extend
picking sequence mechanisms, standard tools from the fair allocation literature
to ensure approximate envy-freeness (typically envy-freeness up to one item, or
EF1). However, fairness often comes at the cost of decreased efficiency. To
overcome this challenge, we carefully select approximately optimal picking
sequence orders. Applying a relaxation of submodularity, $\gamma$-weak
submodularity, we show our Greedy Reviewer Round Robin (GRRR) approach is EF1
and yields a ${(1+\gamma)}$-approximation to the maximum welfare attainable by
a round-robin picking sequence mechanism under any order. We present a weighted
picking sequence mechanism called FairSequence that targets the Weighted EF1
criterion to offer fairness in a more general setting. Using data from three
conferences, we show that FairSequence runs an order of magnitude faster and
provides approximate envy-freeness guarantees that are violated by existing
approaches. Its simple design also makes it very flexible to new assignment
constraints. FairSequence is available in the OpenReview conference management
platform, giving conference organizers access to faster reviewer assignment
with high welfare and envy-freeness guarantees.
