The prospect of finding love may be scary but the prospect of committing to a relationship for the rest of your life is almost certainly scary. The secretary problem is a parallel to romantic decision making where an individual decides when to be satisfied with a selection choice in the face of uncertain future options. However, the secretary problem and its variations still do not provide a pr...

The Sliding Window Secretary Problem allows a window of choices to the Classical Secretary Problem, in which there is the option to choose the previous K choices immediately prior to the current choice. We consider a case of this sequential choice problem in which the interviewer has a finite, known number of choices and can only discern the relative ranks of choices, and in which every permuta...

The secretary problem became one of the most prominent online selection problems due to its numerous applications in online mechanism design. The task is to select a maximumweight subset of elements subject to given constraints, where elements arrive one-by-one in random order, revealing a weight upon arrival. The decision whether to select an element has to be taken immediately after its arriv...

We prove that for every proper minor-closed class M of Fp-representable matroids, there exists a O(1)-competitive algorithm for the matroid secretary problem on M. This result relies on the extremely powerful matroid minor structure theory being developed by Geelen, Gerards and Whittle. We also note that for asymptotically almost all matroids, the matroid secretary algorithm that selects a rand...

In the classical secretary problem the decision maker can only observe the relative ranks of the items presented. Recently, Ferguson building on ideas of Stewart showed that, in a game theoretic sense, 'there is no advantage if the actual values of the random variables underlying the relative ranks can be observed (game of googol). We extend this to the case where the number of items is unknown...

A version of the classical secretary problem is studied, in which one is interested in selecting one of the b best out of a group of n differently ranked persons who are presented one by one in a random order. It is assumed that b ≥ 1 is a preassigned number. It is known, already for a long time, that for the optimal policy one needs to compute b position thresholds, for instance via backwards ...

In the online random-arrival model, an algorithm receives a sequence of n requests that arrive in a random order. The algorithm is expected to make an irrevocable decision with regard to each request based only on the observed history. We consider the following natural extension of this model: each request arrives k times, and the arrival order is a random permutation of the kn arrivals; the al...

In 1963, Dynkin introduced the secretary problem [6]. In this problem, an algorithm is presented with n positive values, one by one. After each value, the algorithm must either accept or reject the value, where all decisions are final. The algorithm can only pick one value, and the goal is to pick the maximum value in the sequence. The name for this problem arises from a situation where n candi...