Class Fairness in Online Matching

We initiate the study of fairness among classes agents in online bipartite matching where there is a given set offline vertices (aka agents) and another items) that arrive must be matched irrevocably upon arrival. In this setting, are partitioned into required to fair with respect classes. adopt popular notions (e.g. envy-freeness, proportionality, maximin share) their relaxations setting deterministic randomized algorithms for indivisible items (leading integral matchings) divisible fractional matchings). For items, we propose an adaptive-priority-based algorithm, MATCH-AND-SHIFT, prove it achieves (1/2)-approximation both class envy-freeness up one item share fairness, show each guarantee tight. design water-filling-based EQUAL-FILLING, (1-1/e)-approximation proportionality; (1-1/e) tight proportionality establish 3/4 upper bound on envy-freeness.