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.
|Number of pages||4|
|Journal||ELECTRONIC COMMUNICATIONS IN PROBABILITY|
|Publication status||Published - 2010|
|MoE publication type||A1 Journal article-refereed|
- Best choice problem
- Partial order
- Secretary problem