A Simple Algorithm for Dynamic Carpooling with Recourse

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].