For the online transportation problem with $m$ server sites, it has long been known that the competitive ratio of any deterministic algorithm is at least $2m-1$. Kalyanasundaram and Pruhs conjectured in 1998 that a deterministic $(2m-1)$-competitive algorithm exists for this problem, a conjecture that has remained open for over two decades. In this paper, we propose a new deterministic algorithm named Subtree-Decomposition for the online transportation problem and show that it achieves a competitive ratio of at most $8m-5$. This is the first $O(m)$-competitive deterministic algorithm, coming close to the lower bound of $2m-1$ within a constant factor.

翻译：对于具有 $m$ 个服务器站点的在线运输问题，长期以来已知任何确定性算法的竞争比至少为 $2m-1$。Kalyanasundaram 和 Pruhs 在 1998 年猜想存在一种针对该问题的确定性 $(2m-1)$-竞争算法，这一猜想已悬置超过二十年。本文中，我们提出了一种名为 Subtree-Decomposition 的新确定性算法用于在线运输问题，并证明其竞争比至多为 $8m-5$。这是首个 $O(m)$-竞争的确定性算法，在常数因子内接近 $2m-1$ 的下界。