Related papers: Packing Returning Secretaries
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…
We present a number of positive and negative results for variants of the matroid secretary problem. Most notably, we design a constant-factor competitive algorithm for the "random assignment" model where the weights are assigned randomly to…
The secretary problem is a classic model for online decision making. Recently, combinatorial extensions such as matroid or matching secretary problems have become an important tool to study algorithmic problems in dynamic markets. Here the…
Suppose that $n$ items arrive online in random order and the goal is to select $k$ of them such that the expected sum of the selected items is maximized. The decision for any item is irrevocable and must be made on arrival without knowing…
We study a twist on the classic secretary problem, which we term the secretary ranking problem: elements from an ordered set arrive in random order and instead of picking the maximum element, the algorithm is asked to assign a rank, or…
In a matroid secretary problem, one is presented with a sequence of objects of various weights in a random order, and must choose irrevocably to accept or reject each item. There is a further constraint that the set of items selected must…
We define and study a new variant of the secretary problem. Whereas in the classic setting multiple secretaries compete for a single position, we study the case where the secretaries arrive one at a time and are assigned, in an on-line…
In the matroid secretary problem, the elements of a matroid $\mathcal{M}$ arrive in random order. Once we observe an item we need to irrevocably decide whether or not to accept it. The set of selected elements should form an independent set…
For many online problems, it is known that the uniform arrival order enables the design of algorithms with much better performance guarantees than under worst-case. The quintessential example is the secretary problem. If the sequence of…
The value maximization version of the secretary problem is the problem of hiring a candidate with the largest value from a randomly ordered sequence of candidates. In this work, we consider a setting where predictions of candidate values…
In classical secretary problems, a sequence of $n$ elements arrive in a uniformly random order, and we want to choose a single item, or a set of size $K$. The random order model allows us to escape from the strong lower bounds for the…
We study various generalizations of the secretary problem with submodular objective functions. Generally, a set of requests is revealed step-by-step to an algorithm in random order. For each request, one option has to be selected so as to…
Most prior work on online matching problems has been with the flexibility of keeping some vertices unmatched. We study three related online matching problems with the constraint of matching every vertex, i.e., with no rejections. We adopt a…
In the classical secretary problem, $n$ ranked items arrive one by one, and each item's rank relative to its predecessors is noted. The observer must select or reject each item as it arrives, with the object of selecting the item of highest…
This paper studies an online trading variant of the classical secretary problem, called secretary problem variant trading (SPVT), from the perspective of an intermediary who facilitates trade between a seller and $n$ buyers (collectively…
In the matroid secretary problem, elements $N := [n]$ of a matroid $\mathcal{M} \subseteq 2^N$ arrive in random order. When an element arrives, its weight is revealed and a choice must be made to accept or reject the element, subject to the…
In the setting of online algorithms, the input is initially not present but rather arrive one-by-one over time and after each input, the algorithm has to make a decision. Depending on the formulation of the problem, the algorithm might be…
The secretary and the prophet inequality problems are central to the field of Stopping Theory. Recently, there has been a lot of work in generalizing these models to multiple items because of their applications in mechanism design. The most…
In the secretary problem we are faced with an online sequence of elements with values. Upon seeing an element we have to make an irrevocable take-it-or-leave-it decision. The goal is to maximize the probability of picking the element of…
In this paper, we investigate two variants of the secretary problem. In these variants, we are presented with a sequence of numbers $X_i$ that come from distributions $\mathcal{D}_i$, and that arrive in either random or adversarial order.…