Laminar Matroid Secretary: Greedy Strikes Back

TL;DR

This paper demonstrates that a straightforward greedy algorithm achieves a 4.75 probability-competitiveness for the Laminar Matroid Secretary Problem, surpassing previous algorithms based on forbidden sets.

Contribution

It introduces a simple greedy approach that improves the competitive ratio for the problem over prior methods.

Findings

Greedy algorithm achieves 4.75-competitive ratio.

Improves upon previous 5.196-competitive algorithms.

Simplifies the approach to the Laminar Matroid Secretary Problem.

Abstract

We show that a simple greedy algorithm is $4.75$ probability-competitive for the Laminar Matroid Secretary Problem, improving the $3\sqrt{3} \approx 5.196$-competitive algorithm based on the forbidden sets technique (Soto, Turkieltaub, and Verdugo, 2018).