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 ∈ V |deg_H^+(v) - 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].