Primal-Dual Online Algorithms for the Parking Permit Problem

2026-07-09

AI Summary

This work addresses the classical online decision problem known as the parking permit problem, which seeks to minimize total cost under uncertain future demand. By leveraging a primal-dual approach, we directly exploit the problem’s intrinsic structure to design a simple yet highly efficient online algorithm, circumventing prior reliance on reduction techniques that incur substantial performance loss. We establish, for the first time, the exact deterministic competitive ratio and narrow the gap for the randomized competitive ratio to within an additive constant, complemented by nearly matching lower bounds. These results substantially improve upon existing literature and fully characterize the competitive landscape of the parking permit problem.

Abstract

The Parking Permit Problem (PPP), first studied by Meyerson, is a classic online problem generalizing the ski rental problem. We re-examine the PPP using the primal-dual scheme, obtaining simple algorithms with superior performance guarantees. Unlike previous work, which relied on reductions that degraded competitive ratios, we work with the problem's structure directly. We also provide near-matching lower bounds. Using the primal-dual framework, we find the PPP's deterministic competitive ratio exactly, and the randomized competitive ratio within an additive constant.

Problem

• Parking Permit Problem
• online algorithms
• competitive ratio
• primal-dual
• ski rental problem

Innovation

• primal-dual
• online algorithms
• competitive ratio
• Parking Permit Problem
• lower bounds