FairColor: An efficient algorithm for the Balanced and Fair Reviewer Assignment Problem

As the volume of submitted papers continues to rise, ensuring a fair and accurate assignment of manuscripts to reviewers has become increasingly critical for academic conference organizers. Given the paper-reviewer similarity scores, this study introduces the Balanced and Fair Reviewer Assignment Problem (BFRAP), which aims to maximize the overall similarity score (efficiency) and the minimum paper score (fairness) subject to coverage, load balance, and fairness constraints. Addressing the challenges posed by these constraints, we conduct a theoretical investigation into the threshold conditions for the problem's feasibility and optimality. To facilitate this investigation, we establish a connection between BFRAP, defined over m reviewers, and the Equitable m-Coloring Problem. Building on this theoretical foundation, we propose FairColor, an algorithm designed to retrieve fair and efficient assignments. We compare FairColor to Fairflow and FairIR, two state-of-the-art algorithms designed to find fair assignments under similar constraints. Empirical experiments were conducted on four real and two synthetic datasets involving (paper, reviewer) matching scores ranging from (100,100) to (10124,5880). Results demonstrate that FairColor is able to find efficient and fair assignments quickly compared to Fairflow and FairIR. Notably, in the largest instance involving 10,124 manuscripts and 5680 reviewers, FairColor retrieves fair and efficient assignments in just 67.64 s. This starkly contrasts both other methods, which require significantly longer computation times (45 min for Fairflow and 3 h 24 min for FairIR), even on more powerful machines. These results underscore FairColor as a promising alternative to current state-of-the-art assignment techniques.