A Nearly Optimal Deterministic Algorithm for Online Transportation Problem

TL;DR

This paper introduces a new deterministic algorithm for the online transportation problem that achieves a competitive ratio close to the theoretical lower bound, improving the efficiency of online solutions.

Contribution

It presents the Subtree-Decomposition algorithm, the first $O(m)$-competitive deterministic approach, narrowing the gap to the long-standing lower bound.

Findings

Achieves a competitive ratio of at most 8m-5

First $O(m)$-competitive deterministic algorithm for the problem

Close to the conjectured optimal ratio of 2m-1

Abstract

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.