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arXiv · 2508.08381

Competitive Online Transportation Simplified

Stephen Arndt·Benjamin Moseley·Kirk Pruhs·Marc Uetz
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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.

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Stephen Arndt, Benjamin Moseley, Kirk Pruhs, Marc Uetz. 2025-08-11. Competitive Online Transportation Simplified. https://arxiv.org/abs/2508.08381

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