Partially ordered secretaries
Artikel i vetenskaplig tidskrift, 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.


Ragnar Freij

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Johan Wästlund

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Electronic Communications in Probability

1083-589X (ISSN)

Vol. 15 504-507



Sannolikhetsteori och statistik

Diskret matematik

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