An Improved Algorithm for Open Online Dial-a-Ride

TL;DR

This paper introduces a new parameterized online algorithm for the open dial-a-ride problem in metric spaces, achieving a competitive ratio of approximately 2.618, which improves upon previous bounds.

Contribution

The paper presents a novel parameterized algorithm with improved competitive ratio bounds for open online dial-a-ride in general metric spaces and the real line.

Findings

Achieves a competitive ratio of about 2.618 with specific parameters.

Provides a lower bound of 2.457 for the algorithm's competitive ratio.

Improves previous bounds for the problem in various metric spaces.

Abstract

We consider the open online dial-a-ride problem, where transportation requests appear online in a metric space and need to be served by a single server. The objective is to minimize the completion time until all requests have been served. We present a new, parameterized algorithm for this problem and prove that it attains a competitive ratio of $1 + \varphi \approx 2.618$ for some choice of its parameter, where $\varphi$ is the golden ratio. This improves the best known bounds for open online dial-a-ride both for general metric spaces as well as for the real line. We also give a lower bound of~$2.457$ for the competitive ratio of our algorithm for any parameter choice.