Year: 2025
Type: conference-paper
Abstract: Given an edge-colored graph, the goal of the proportional fair matching problem is to find a maximum weight matching while ensuring proportional representation (with respect to the number of edges) of each color. The colors may correspond to demographic groups or other protected traits where we seek to ensure roughly equal representation from each group. It is known that, assuming ETH, it is impossible to approximate the problem with ℓ colors in time subexponential in ℓ even on unweighted path graphs. Further, even determining the existence of a non-empty matching satisfying proportionality is NP-Hard. To overcome this hardness, we relax the stringent proportional fairness constraints to a probabilistic notion. We introduce a notion we call δ-PʀᴏʙᴀʙʟʏFᴀɪʀ where we ensure proportionality up to a factor of at most (1 ± δ) for some small δ > 0 with high probability. The violation δ can be brought arbitrarily close to 0 for some good instances with large values of matching size. We propose and analyze simple and fast algorithms for bipartite graphs that achieve constant-factor approximation guarantees, and return a δ-PʀᴏʙᴀʙʟʏFᴀɪʀ matching.
Institutions: University of Maryland, College Park, Columbia University
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
SDG: Reduced inequalities
Open Access status: diamond
Funder: National Science Foundation
OpenAlex ID: W4409364505