Related papers: Formal Barriers to Simple Algorithms for the Matro…
We study the submodular secretary problem with a cardinality constraint. In this problem, $n$ candidates for secretaries appear sequentially in random order. At the arrival of each candidate, a decision maker must irrevocably decide whether…
For two matroids $\mathcal{M}_1$ and $\mathcal{M}_2$ defined on the same ground set $E$, the online matroid intersection problem is to design an algorithm that constructs a large common independent set in an online fashion. The algorithm is…
In the \textit{Matroid Secretary Problem} (MSP), the elements of the ground set of a Matroid are revealed on-line one by one, each together with its value. An algorithm for the MSP is \textit{Matroid-Unknown} if, at every stage of its…
The Adwords and Online Bipartite Matching problems have enjoyed a renewed attention over the past decade due to their connection to Internet advertising. Our community has contributed, among other things, new models (notably stochastic) and…
In the matroid buyback problem, an algorithm observes a sequence of bids and must decide whether to accept each bid at the moment it arrives, subject to a matroid constraint on the set of accepted bids. Decisions to reject bids are…
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…
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…
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…
This article studies two notions of generalized matroid representations motivated by algorithmic information theory and cryptographic secret sharing. The first (entropic representability) involves discrete random variables, while the second…
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…
We study matroid prophet inequalities when distributions are unknown and accessible only through samples. While single-sample prophet inequalities for special matroids are known, no constant-factor competitive algorithm with even a…
We study secretary problems in settings with multiple agents. In the standard secretary problem, a sequence of arbitrary awards arrive online, in a random order, and a single decision maker makes an immediate and irrevocable decision…
Online Bipartite Matching with random user arrival is a fundamental problem in the online advertisement ecosystem. Over the last 30 years, many algorithms and impossibility results have been developed for this problem. In particular, the…
A matroid $\mathcal{M}$ on a set $E$ of elements has the $\alpha$-partition property, for some $\alpha>0$, if it is possible to (randomly) construct a partition matroid $\mathcal{P}$ on (a subset of) elements of $\mathcal{M}$ such that…
We revisit the knapsack-secretary problem (Babaioff et al.; APPROX 2007), a generalization of the classic secretary problem in which items have different sizes and multiple items may be selected if their total size does not exceed the…
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…
Many online problems are studied in stochastic settings for which inputs are samples from a known distribution, given in advance, or from an unknown distribution. Such distributions model both beyond-worst-case inputs and, when given,…
In learning-augmented online algorithms, predictions are usually valued for what they say: a value estimate, a solution, or an algorithmic recommendation. This paper shows that predictions can also be valuable solely due to their arrival…
Maintaining a maximum bipartite matching online while minimizing recourse/augmentations is a well studied problem, motivated by content delivery, job scheduling, and hashing. A breakthrough result of Bernstein, Holm, and Rotenberg…
In the Online Machine Covering problem jobs, defined by their sizes, arrive one by one and have to be assigned to $m$ parallel and identical machines, with the goal of maximizing the load of the least-loaded machine. In this work, we study…