A Nearly Optimal Deterministic Algorithm for Online Transportation Problem

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.