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.

翻译：在线运输问题的设定是一个度量空间$M$，其中分布着$m$个容量各异的停车场。随着时间的推移，汽车陆续到达$M$，且必须在到达时被不可撤销地分配至某个停车场，同时需满足停车场的容量限制。目标是最小化汽车行驶的总距离。1998年，Kalyanasundaram与Pruhs猜想在线运输问题存在一个确定性算法，其竞争比为$(2m-1)$，这与更简单的在线度量匹配问题的最优竞争比相匹配。近期，Harada与Itoh提出了首个$O(m)$竞争比的确定性算法用于在线运输问题。我们的贡献在于提出了一种替代性的算法设计与分析，我们认为该方法更为简洁。