We propose a new deterministic algorithm called Subtree-Decomposition for the online transportation problem and show that the algorithm is $(8m-5)$-competitive, where $m$ is the number of server sites. It has long been known that the competitive ratio of any deterministic algorithm is lower bounded by $2m-1$ for this problem. On the other hand, the conjecture proposed by Kalyanasundaram and Pruhs in 1998 asking whether a deterministic $(2m-1)$-competitive algorithm exists for the online transportation problem has remained open for over two decades. The upper bound on the competitive ratio, $8m-5$, which is the result of this paper, is the first to come close to this conjecture, and is the best possible within a constant factor.

翻译：本文提出了一种名为Subtree-Decomposition的新型确定性算法用于在线运输问题，并证明该算法具有$(8m-5)$的竞争比，其中$m$表示服务器站点的数量。长期以来，已知该问题的任何确定性算法的竞争比下界为$2m-1$。另一方面，Kalyanasundaram与Pruhs于1998年提出的猜想——是否存在确定性$(2m-1)$竞争比算法解决在线运输问题——已悬置二十余年。本文得出的竞争比上界$8m-5$首次接近该猜想，且在常数因子范围内达到最优。