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Online matching markets (OMMs) are commonly used in today’s world to pair agents from two parties (whom we will call offline and online agents) for mutual benefit. However, studies have shown that the algorithms making decisions in these OMMs often leave disparities in matching rates, especially for offline agents. In this article, we propose online matching algorithms that optimize for either individual or group-level fairness among offline agents in OMMs. We present two linear-programming (LP) based sampling algorithms, which achieve competitive ratios at least 0.725 for individual fairness maximization and 0.719 for group fairness maximization. We derive further bounds based on fairness parameters, demonstrating conditions under which the competitive ratio can increase to 100%. There are two key ideas helping us break the barrier of 1-1/𝖾~ 63.2% for competitive ratio in online matching. One is boosting , which is to adaptively re-distribute all sampling probabilities among only the available neighbors for every arriving online agent. The other is attenuation , which aims to balance the matching probabilities among offline agents with different mass allocated by the benchmark LP. We conduct extensive numerical experiments and results show that our boosted version of sampling algorithms are not only conceptually easy to implementmore »but also highly effective in practical instances of OMMs where fairness is a concern.« less

We consider online resource allocation under a typical non-profit setting, where limited or even scarce resources are administered by a not-for-profit organization like a government. We focus on the internal-equity by assuming that arriving requesters are homogeneous in terms of their external factors like demands but heterogeneous for their internal attributes like demographics. Specifically, we associate each arriving requester with one or several groups based on their demographics (i.e., race, gender, and age), and we aim to design an equitable distributing strategy such that every group of requesters can receive a fair share of resources proportional to a preset target ratio. We present two LP-based sampling algorithms and investigate them both theoretically (in terms of competitive-ratio analysis) and experimentally based on real COVID-19 vaccination data maintained by the Minnesota Department of Health. Both theoretical and numerical results show that our LP-based sampling strategies can effectively promote equity, especially when the arrival population is disproportionately represented, as observed in the early stage of the COVID-19 vaccine rollout.

Potassium‐ion batteries (KIBs) are considered as the potential energy storage devices due to the abundant reserves and low cost of potassium. In the past decade, research on KIBs has generally focused on electrode materials. However, since electrolytes also play a key role in determining the cell performance, this review summarizes recent advances in KIB electrolytes and design strategies. Specifically, the review includes five parts. First, the organic liquid electrolyte is the most widely used type for KIBs. Its two major components, salts and solvents, have a huge impact on the formation of the solid electrolyte interphase and the performance of KIBs. Changes in salts/solvents, the introduction of additives, and the concentration increase all have a positive effect on organic liquid electrolytes. Second, the design of water‐in‐salt electrolytes can effectively widen the narrow electrochemical stability window of aqueous electrolytes. Third, despite the appealing properties, the ionic liquid electrolytes have not been widely applied due to its high cost. Fourth, the solid‐state electrolytes have drawn much attention due to high safety, and current research has been working on improving their ionic conductivity at room temperature. Lastly, perspectives are provided to support the future development of suitable electrolytes for high‐performance KIBs.