Computational bounds on randomized algorithms for online bin stretching

TL;DR

This paper develops computational methods to design and analyze randomized algorithms for online bin stretching, providing bounds on their performance and improving upon deterministic solutions.

Contribution

It introduces linear programming-based techniques to construct lower bounds and design better randomized algorithms for online bin stretching.

Findings

Linear programming bounds for randomized algorithms

New randomized algorithms outperform deterministic ones

Lower bounds for restricted randomized algorithms

Abstract

A frequently studied performance measure in online optimization is competitive analysis. It corresponds to the worst-case ratio, over all possible inputs of an algorithm, between the performance of the algorithm and the optimal offline performance. However, this analysis may be too pessimistic to give valuable insight on a problem. Several workarounds exist, such as randomized algorithms. This paper aims to propose computational methods to construct randomized algorithms and to bound their performance on the classical online bin stretching problem. A game theory method is adapted to construct lower bounds on the performance of randomized online algorithms via linear programming. Another computational method is then proposed to construct randomized algorithms which perform better than the best deterministic algorithms known. Finally, another lower bound method for a restricted class of randomized algorithm for this problem is proposed.