Journal article, 2010

The elements of a finite nonempty partially ordered set are exposed at independent uniform times in [0, 1] to a selector who, at any given time, can see the structure of the induced partial order on the exposed elements. The selector’s task is to choose online a maximal element.
This generalizes the classical linear order secretary problem, for which it is known that the selector can succeed with probability 1=e and that this is best possible.
We describe a strategy for the general problem that achieves success probability at least 1=e for an arbitrary partial order.

Best choice problem

Secretary problem

Partial order.

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

1083-589X (ISSN)

Vol. 15 504-507Computational Mathematics

Probability Theory and Statistics

Discrete Mathematics