A Simple Algorithm for Dynamic Carpooling with Recourse

TL;DR

This paper introduces a simple, improved algorithm for maintaining balanced orientations in a fully-dynamic graph with edges arriving and departing, relevant for dynamic carpooling systems, ensuring low discrepancy at all times.

Contribution

The paper presents a straightforward algorithm for the dynamic graph orientation problem with recourse, simplifying and enhancing previous results by Gupta et al.

Findings

Algorithm maintains low discrepancy in dynamic graphs.

Simplifies previous cycle-based approaches.

Improves bounds on recourse and discrepancy.

Abstract

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].