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 maxv∈V∣degH+(v)−degH−(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].
@article{arxiv.2411.07553,
title = {A Simple Algorithm for Dynamic Carpooling with Recourse},
author = {Yuval Efron and Shyamal Patel and Cliff Stein},
journal= {arXiv preprint arXiv:2411.07553},
year = {2024}
}