Deterministic $(2k-1)$-competitive online transportation algorithm

Determine whether online metric transportation admits a deterministic $(2k-1)$-competitive algorithm, matching the known lower bound and yielding a competitive guarantee independent of the total capacity.

Background

The online metric transportation problem assigns sequentially arriving requests to $k$ capacitated server locations in a metric space. The competitive ratio is measured against an offline optimum that knows the entire request sequence, and the desired bound should depend on the number of server locations $k$ rather than the total capacity $n$.

A deterministic $(2k-1)$ lower bound is known, and the cited conjecture proposes that this lower bound is achievable. Prior to the paper, deterministic upper bounds had reached $8k-7$; the paper improves this to approximately $6.6604k-2.89$ but does not establish the conjectured exact bound.