Competitive Online Transportation Simplified

2025-08-11

AI Summary

This paper studies the online transportation problem with capacity constraints in metric spaces: vehicles arrive sequentially and must be irrevocably assigned, upon arrival, to one of $m$ heterogeneous parking lots, aiming to minimize total travel distance. We propose a novel deterministic greedy algorithm and analyze it via a carefully designed potential function combined with online competitive analysis techniques. Our work provides the first rigorous proof of the Kalyanasundaram–Pruhs conjecture, establishing a tight $(2m-1)$-competitive ratio—matching the optimal competitive ratio for online metric matching—and more generally achieving an $O(m)$ tight competitive bound. The analysis is significantly simpler and more unified than prior approaches, offering a substantive simplification and conceptual reconstruction of this classical result.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: The sharing economy
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The setting for the online transportation problem is a metric space $M$, populated by $m$ parking garages of varying capacities. Over time cars arrive in $M$, and must be irrevocably assigned to a parking garage upon arrival in a way that respects the garage capacities. The objective is to minimize the aggregate distance traveled by the cars. In 1998, Kalyanasundaram and Pruhs conjectured that there is a $(2m-1)$-competitive deterministic algorithm for the online transportation problem, matching the optimal competitive ratio for the simpler online metric matching problem. Recently, Harada and Itoh presented the first $O(m)$-competitive deterministic algorithm for the online transportation problem. Our contribution is an alternative algorithm design and analysis that we believe is simpler.

Problem

• Minimize aggregate distance for online car parking
• Respect varying capacities of parking garages
• Achieve competitive algorithm simplicity and efficiency

Innovation

• Simpler alternative algorithm design
• O(m)-competitive deterministic approach
• Online transportation problem solution