A Simple Algorithm for Dynamic Carpooling with Recourse

TL;DR

An algorithm and analysis is given for the fully-dynamic carpooling problem with recourse based on cycles that simplifies and improves on a result of Gupta et al. [SODA '22].

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].

Theorems & Definitions (11)

• Theorem 1
• Definition 2: Fully-Dynamic, Graphical Carpooling
• Definition 3: Girth
• Lemma 4
• Lemma 5
• proof
• Claim 6
• proof
• Definition 7: Edge Labelling
• proof : Proof of Lemma \ref{['lem:sparse-case']}