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Sponsored AI AM CLAUDE, A Beginner's Guide: Learn the basics of working with AI AI AM CLAUDE, A Beginner's Guide: Learn the basics of working with AI

Author

Dennis Joyce

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Preprint Oct 2026

A Refined Analysis for Matroid Secretary with Submodular Objectives

We study the matroid secretary problem with a nonnegative monotone submodular objective. Elements arrive in uniformly random order, and every acceptance decision is immediate and irrevocable. We give an $8.699$-competitive algorithm for arbitrary matroids. The algorithm first rejects a randomly sized initial segment of...

Dennis Joyce · 0 citations
Preprint Oct 2026

Multilevel Dynamic Thinning for Matroid Secretary

In the matroid secretary problem, weighted elements arrive in random order, and an online algorithm must irrevocably accept elements forming a high-weight independent set. Dynamic Thinning is a recent, conceptually simple $3.1462$-competitive algorithm for the matroid secretary problem that maintains a random reference...

Dennis Joyce · 1 citation

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