English

The SBP Algorithm for Maximizing Revenue in Online Dial-a-Ride

Data Structures and Algorithms 2019-12-16 v1

Abstract

In the Online-Dial-a-Ride Problem (OLDARP) a server travels through a metric space to serve requests for rides. We consider a variant where each request specifies a source, destination, release time, and revenue that is earned for serving the request. The goal is to maximize the total revenue earned within a given time limit. We prove that no non-preemptive deterministic online algorithm for OLDARP can be guaranteed to earn more than twice the revenue earned by an optimal offline solution. We then investigate the \textsc{segmented best path} (SBPSBP) algorithm of~\cite{atmos17} for the general case of weighted graphs. The previously-established lower and upper bounds for the competitive ratio of SBPSBP are 4 and 6, respectively, under reasonable assumptions about the input instance. We eliminate the gap by proving that the competitive ratio is 5 (under the same reasonable assumptions). We also prove that when revenues are uniform, SBPSBP has competitive ratio 4. Finally, we provide a competitive analysis of SBPSBP on complete bipartite graphs.

Keywords

Cite

@article{arxiv.1912.06300,
  title  = {The SBP Algorithm for Maximizing Revenue in Online Dial-a-Ride},
  author = {Ananya Christman and Christine Chung and Nicholas Jaczko and Tianzhi Li and Scott Westvold and Xinyue Xu},
  journal= {arXiv preprint arXiv:1912.06300},
  year   = {2019}
}
R2 v1 2026-06-23T12:44:46.617Z