In typical online matching problems, the goal is to maximize the number of matches. This paper studies online bipartite matching from the perspective of group-level fairness, and the goal is to balance the number of matches made across different groups of online nodes. We assume that an online node's group belongings are revealed upon arrival, and measure performance based on the group with the smallest fraction of its nodes matched at the end. We distinguish between two different objectives: long-run fairness, where the algorithm is audited for its fairness over many realizations from the same instance; and short-run fairness, where the algorithm is audited for its fairness on a single realization. We focus on the known-IID model of online arrivals and analyze, under both objectives, the competitive ratio for two classes of algorithms: non-rejecting algorithms, which must match an online node as long as a neighbor is available; and general online algorithms , which are allowed to reject online nodes to improve fairness . For long-run fairness, we analyze two online algorithms (sampling and pooling ) which establish asymptotic optimality across many different regimes (no specialized supplies, no rare demand types, or imbalanced supply/demand). By contrast, outside all of these regimes, we show that the competitive ratio for online algorithms is between 0.632 and 0.732. For short-run fairness, we focus on the case of a complete bipartite graph and show that the competitive ratio for online algorithms is between 0.863 and 0.942; we also derive a probabilistic rejection algorithm which is asymptotically optimal as total demandincreases .
We consider the allocation of limited resources to heterogeneous customers who arrive in an online fashion. We would like to allocate the resources "fairly", so that no group of customers is marginalized in terms of their overall service rate. We study whether this is possible to do so in an online fashion, and if so, what a good online allocation policy is. We model this problem using online bipartite matching under stationary arrivals, a fundamental model in the literature typically studied under the objective of maximizing the total number of customers served. We instead study the objective of maximizing the minimum service rate across all groups, and propose two notions of fairness: long-run and short-run . For these fairness objectives, we analyze how competitive online algorithms can be, in comparison to offline algorithms which know the sequence of demands in advance . For long-run fairness, we propose two online heuristics (Sampling and Pooling ) which establish asymptotic optimality in different regimes (no specialized supplies, no rare demand types, or imbalanced supply/demand). By contrast, outside all of these regimes, we show that the competitive ratio of online algorithms is between 0.632 and 0.732. For short-run fairness, we show for complete bipartite graphs that the competitive ratio of online algorithms is between 0.863 and 0.942; we also derive a probabilistic rejection algorithm which is asymptotically optimal in the total demand. Depending on the overall scarcity of resources, either our Sampling or Pooling heuristics could be desirable. The most difficult situation for online allocation occurs when the total supply is just enough to serve the total demand. We simulate our algorithms on a public ride-hailing dataset, which both demonstrates the efficacy of our heuristics and validates our managerial insights .
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In typical online matching problems, the goal is to maximize the number of matches. This paper studies online bipartite matching from the perspective of group-level fairness, and the goal is to balance the number of matches made across different groups of online nodes. We assume that an online node's group belongings are revealed upon arrival, and measure performance based on the group with the smallest fraction of its nodes matched at the end. We distinguish between two different objectives:
We consider the allocation of limited resources to heterogeneous customers who arrive in an online fashion. We would like to allocate the resources "fairly", so that no group of customers is marginalized in terms of their overall service rate. We study whether this is possible to do so in an online fashion, and if so, what a good online allocation policy is. We model this problem using online bipartite matching under stationary arrivals, a fundamental model in the literature typically studied under the objective of maximizing the total number of customers served. We instead study the objective of maximizing the minimum service rate across all groups, and propose two notions of fairness:
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fairness, where the algorithm is audited for its fairness on a single realization. We focus on the known-IID model of online arrivals and analyze, under both objectives, the competitive ratio for two classes of algorithms: non-rejecting algorithms, which must match an online node as long as a neighbor is available; and general online algorithms , which are allowed to reject online nodes to improve fairness
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in the total demand. Depending on the overall scarcity of resources, either our Sampling or Pooling heuristics could be desirable. The most difficult situation for online allocation occurs when the total supply is just enough to serve the total demand. We simulate our algorithms on a public ride-hailing dataset, which both demonstrates the efficacy of our heuristics and validates our managerial insights