Resource Augmentation Analysis of the Greedy Algorithm for the Online Transportation Problem

TL;DR

This paper analyzes the online transportation problem in a metric space, demonstrating that a greedy algorithm with augmented garage capacities achieves a competitive ratio approaching 1 as augmentation increases.

Contribution

It introduces a resource augmentation framework for the online transportation problem and proves the competitive ratio of the greedy algorithm with capacity augmentation.

Findings

Greedy algorithm with capacity augmentation is (1 + 2/(k-2))-competitive for k ≥ 3.

Increasing capacity augmentation improves the competitive ratio.

The analysis provides bounds on the performance of the greedy approach.

Abstract

We consider the online transportation problem set in a metric space containing parking garages of various capacities. Cars arrive over time, and must be assigned to an unfull parking garage upon their arrival. The objective is to minimize the aggregate distance that cars have to travel to their assigned parking garage. We show that the natural greedy algorithm, augmented with garages of $k\ge3$ times the capacity, is $\left(1 + \frac{2}{k-2}\right)$-competitive.