Matroid secretary problem solved with efficient new algorithm
Settling the Matroid Secretary Problem
Data Structures and Algorithms
Summary
The matroid secretary problem involves making the best choices from a sequence of options that arrive one by one, without knowing the future. The authors present a new algorithm that guarantees a solution close to the best possible, based only on comparisons and a way to check if choices fit certain rules. Their method runs efficiently and uses a mathematical approach called matroids, which generalize ideas like spanning trees or matchings. This settles a long-standing question about how well this problem can be solved.
What this means in practice
- •For network schedulers: Assign resources to tasks arriving unpredictably with provable performance guarantees based on matroid constraints.
- •For logistics planners: Make near-optimal real-time decisions on selecting routes or shipments under complex feasibility rules.
A theory result. No direct application yet.
Authors
Zhiyi Huang
Abstract
This paper settles the Matroid Secretary Problem with an $e$-probability-competitive algorithm. The algorithm is ordinal and accesses arrived elements only through comparison and independence oracles, and has expected polynomial time and oracle complexity.