Competitive Online Transportation Simplified

TL;DR

This paper introduces a simpler deterministic algorithm for the online transportation problem in metric spaces, improving the understanding of competitive ratios and matching the best known bounds.

Contribution

We present an alternative, simpler deterministic algorithm for the online transportation problem with competitive ratio proportional to the number of garages.

Findings

Achieved an $O(m)$-competitive ratio for the problem.

Provided a new analysis approach simplifying previous algorithms.

Confirmed the conjectured bounds for online transportation algorithms.

Abstract

The setting for the online transportation problem is a metric space $M$, populated by $m$ parking garages of varying capacities. Over time cars arrive in $M$, and must be irrevocably assigned to a parking garage upon arrival in a way that respects the garage capacities. The objective is to minimize the aggregate distance traveled by the cars. In 1998, Kalyanasundaram and Pruhs conjectured that there is a $(2m-1)$-competitive deterministic algorithm for the online transportation problem, matching the optimal competitive ratio for the simpler online metric matching problem. Recently, Harada and Itoh presented the first $O(m)$-competitive deterministic algorithm for the online transportation problem. Our contribution is an alternative algorithm design and analysis that we believe is simpler.