We give an algorithm for the fully-dynamic carpooling problem with recourse: Edges arrive and depart online from a graph $G$ with $n$ nodes according to an adaptive adversary. Our goal is to maintain an orientation $H$ of $G$ that keeps the discrepancy, defined as $\max_{v \in V} |\text{deg}_H^+(v) - \text{deg}_H^-(v)|$, small at all times. We present a simple algorithm and analysis for this problem with recourse based on cycles that simplifies and improves on a result of Gupta et al. [SODA '22].

翻译：我们针对带补救机制的完全动态拼车问题提出一种算法：在自适应对手策略下，边根据在线方式动态加入或离开具有$n$个节点的图$G$。我们的目标是始终维持$G$的一个定向$H$，使得由$\max_{v \in V} |\text{deg}_H^+(v) - \text{deg}_H^-(v)|$定义的不平衡度保持较小。我们提出了一种基于环路的简单算法及其补救机制分析，该工作简化并改进了Gupta等人[SODA '22]的研究结果。