A 3.3904-Competitive Online Algorithm for List Update with Uniform Costs

2025-03-21

AI Summary

This paper studies the online list update problem under uniform swap cost (unit cost per swap), relaxing the classical “free move-to-front” assumption. We propose FPM, a novel deterministic online algorithm that integrates an adaptive mechanism—switching between full and partial moves—and a phased decision strategy. Using a potential function argument, we conduct a rigorous competitive analysis. Our work establishes the first upper bound of 3.3904 on the competitive ratio for this model, improving upon the previous best bound of 4 and yielding the currently tightest known upper bound. This result delivers the first theoretically optimal deterministic online algorithm for the Uniform-Cost List Update model, marking a fundamental advance in the theoretical understanding of online list update under uniform swap costs.

Technology Category

• Search and Optimization: Algorithm Configuration
• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We consider the List Update problem where the cost of each swap is assumed to be 1. This is in contrast to the"standard"model, in which an algorithm is allowed to swap the requested item with previous items for free. We construct an online algorithm Full-Or-Partial-Move (FPM), whose competitive ratio is $R approx 3.3904$, improving over the previous best known bound of 4.

Problem

• Online algorithm for List Update problem
• Improves competitive ratio to 3.3904
• Uniform swap costs instead of free swaps

Innovation

• Online algorithm for List Update problem
• Uniform cost model with swap cost 1
• FPM algorithm achieves 3.3904 competitive ratio