Strong Algorithms for the Ordinal Matroid Secretary Problem

In the ordinal matroid secretary problem (MSP), candidates do not reveal numerical weights, but decision maker can still discern if a candidate is better than another. An algorithm [Formula: see text] probability-competitive every element from optimum appears with probability in output. This measure stronger standard utility competitiveness. Our main result introduction of technique based on forbidden sets to design algorithms strong ratios many classes. We improve upon guarantees for almost class considered MSP literature. particular, we achieve 4 graphic matroids and laminar matroids. Additionally, modify Kleinberg’s utility-competitive uniform rank order obtain algorithm. also contribute arbitrary