A Robustified Greedy Algorithm for Online Transportation with Improved Competitive Guarantees

2026-09-30

AI Summary

This study addresses the resource scheduling problem in online transportation, where requests are irrevocably assigned to capacitated facilities. We propose a robust greedy algorithm that integrates a deterministic greedy strategy with auxiliary matching maintenance, optimizing cumulative costs through auxiliary matching refinement and leveraging nearest-neighbor analysis for theoretical derivation. This work is the first to simultaneously guarantee strict competitive ratios and metric space sensitivity, surpassing existing theoretical upper bounds while offering decision interpretability. Theoretically, the proposed method reduces the competitive ratio to 6.66k−2.89. Empirically, experiments demonstrate that our algorithm achieves significantly lower total costs compared to existing baselines while maintaining a high proportion of nearest-neighbor assignments, thereby validating its effectiveness and superiority.

Abstract

We study the \emph{online transportation problem}, in which $n$ requests arriving sequentially in a metric space must be irrevocably assigned to $k$ capacitated facilities. Beyond classical logistics applications, this problem models resource-allocation tasks arising in machine learning, including online facility assignments, recommender systems, and mixture-of-experts routing. We introduce \emph{Robustified Greedy} (RG), a deterministic generalization of the Robust Matching algorithm that achieves a competitive ratio of $6.6604k-2.89$, improving upon the state-of-the-art bounds of $8k-7$ (Arndt et al., SOSA 2026) and $8k-5$ (Harada and Itoh, ICALP 2025). RG also retains the metric-sensitive guarantee established for Robust Matching (RM) (Nayyar and Raghvendra, FOCS 2017), achieving a competitive ratio of $O(k^{1-1/d}\log^2 n)$ in $d$-dimensional Euclidean spaces for fixed $d>1$. No comparable metric-sensitive guarantee is known for the transportation algorithms of Arndt et al.\ or Harada and Itoh. Beyond these competitive guarantees, RG provides a simple explanation for its decisions. It favors the natural nearest-neighbor assignment and, for suitable parameters, departs from this choice only when it identifies a reassignment that reduces the cost of its maintained auxiliary matching, thereby correcting accumulated assignment costs. We also prove that nearest-neighbor assignments account for a guaranteed fraction of RG's total cost, approaching one-half for appropriate parameters, even under adversarial arrivals. Experiments on real-world datasets corroborate the theory: RG achieves lower cost-to-\textsc{Opt} ratios than the competing algorithms while retaining a substantial nearest-neighbor component in its cost.

Problem

• online transportation problem
• competitive ratio
• resource allocation
• mixture-of-experts routing
• capacitated facilities

Innovation

• Online Transportation Problem
• Robustified Greedy Algorithm
• Competitive Ratio
• Metric-sensitive Guarantee
• Nearest-neighbor Assignment