相关论文: Matroid Secretary Is Equivalent to Contention Reso…
Contention resolution schemes have proven to be a useful and unifying abstraction for a variety of constrained optimization problems, in both offline and online arrival models. Much of prior work restricts attention to product distributions…
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…
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…
Babaioff et al. [BIK2007] introduced the matroid secretary problem in 2007, a natural extension of the classic single-choice secretary problem to matroids, and conjectured that a constant-competitive online algorithm exists. The conjecture…
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 became one of the most prominent online selection problems due to its numerous applications in online mechanism design. The task is to select a maximum weight subset of elements subject to given constraints, where…
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…
The most well-known conjecture in the context of matroid secretary problems claims the existence of a constant-factor approximation applicable to any matroid. Whereas this conjecture remains open, modified forms of it were shown to be true,…
Online contention resolution scheme (OCRS) is a powerful technique for online decision making, which--in the case of matroids--given a matroid and a prior distribution of active elements, selects a subset of active elements that satisfies…
In the Matroid Secretary Problem, introduced by Babaioff et al. [SODA 2007], the elements of a given matroid are presented to an online algorithm in random order. When an element is revealed, the algorithm learns its weight and decides…
One of the classic problems in online decision-making is the *secretary problem* where to goal is to maximize the probability of choosing the largest number from a randomly ordered sequence. A natural extension allows selecting multiple…
The Matroid Secretary Problem (MSP) is one of the most prominent settings for online resource allocation and optimal stopping. A decision-maker is presented with a ground set of elements $E$ revealed sequentially and in random order. Upon…
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…
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…
The Matroid Secretary Conjecture is a notorious open problem in online optimization. It claims the existence of an $O(1)$-competitive algorithm for the Matroid Secretary Problem (MSP). Here, the elements of a weighted matroid appear…
We study the matroid secretary problems with submodular valuation functions. In these problems, the elements arrive in random order. When one element arrives, we have to make an immediate and irrevocable decision on whether to accept it or…
Random order online contention resolution schemes (ROCRS) are structured online rounding algorithms with numerous applications and links to other well-known online selection problems, like the matroid secretary conjecture. We are interested…
We introduce the notion of an online matroid embedding, which is an algorithm for mapping an unknown matroid that is revealed in an online fashion to a larger-but-known matroid. We establish the existence of such an embedding for binary…
Motivated by the growing interest in correlation-robust stochastic optimization, we investigate stochastic selection problems beyond independence. Specifically, we consider the instructive case of pairwise-independent priors and matroid…
We prove that for every proper minor-closed class $M$ of matroids representable over a prime field, there exists a constant-competitive matroid secretary algorithm for the matroids in $M$. This result relies on the extremely powerful…