相关论文: Combinatorial Prophet Inequalities

Submodular function minimization (SFM) is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint…

We consider the problem of maximizing submodular functions in single-pass streaming and secretaries-with-shortlists models, both with random arrival order. For cardinality constrained monotone functions, Agrawal, Shadravan, and Stein gave a…

We explore a prophet inequality problem, where the values of a sequence of items are drawn i.i.d. from some distribution, and an online decision maker must select one item irrevocably. We establish that $\mathrm{CR}_{\ell}$ the worst-case…

With the rapid growth of data in modern applications, parallel algorithms for maximizing non-monotone submodular functions have gained significant attention. In the parallel computation setting, the state-of-the-art approximation ratio of…

We present an optimal, combinatorial 1-1/e approximation algorithm for monotone submodular optimization over a matroid constraint. Compared to the continuous greedy algorithm (Calinescu, Chekuri, Pal and Vondrak, 2008), our algorithm is…

We consider the problem of maximizing a monotone submodular function under noise. There has been a great deal of work on optimization of submodular functions under various constraints, resulting in algorithms that provide desirable…

In this work we give two new algorithms that use similar techniques for (non-monotone) submodular function maximization subject to a cardinality constraint. The first is an offline fixed parameter tractable algorithm that guarantees a…

In this work we initiate the study of buy-and-sell prophet inequalities. We start by considering what is arguably the most fundamental setting. In this setting the online algorithm observes a sequence of prices one after the other. At each…

Prophet inequalities are a cornerstone in optimal stopping and online decision-making. Traditionally, they involve the sequential observation of $n$ non-negative independent random variables and face irrevocable accept-or-reject choices.…

Prophet inequalities are performance guarantees for online algorithms (a.k.a. stopping rules) solving the following "hiring problem": a decision maker sequentially inspects candidates whose values are independent random numbers and is asked…

We present combinatorial and parallelizable algorithms for maximization of a submodular function, not necessarily monotone, with respect to a size constraint. We improve the best approximation factor achieved by an algorithm that has…

Budget feasible mechanism considers algorithmic mechanism design questions where there is a budget constraint on the total payment of the mechanism. An important question in the field is that under which valuation domains there exist budget…

Submodular functions are a fundamental object of study in combinatorial optimization, economics, machine learning, etc. and exhibit a rich combinatorial structure. Many subclasses of submodular functions have also been well studied and…

During the last decade, the matroid secretary problem (MSP) became one of the most prominent classes of online selection problems. Partially linked to its numerous applications in mechanism design, substantial interest arose also in the…

Optimization problems with set submodular objective functions have many real-world applications. In discrete scenarios, where the same item can be selected more than once, the domain is generalized from a 2-element set to a bounded integer…

We propose a theoretical framework to capture incremental solutions to cardinality constrained maximization problems. The defining characteristic of our framework is that the cardinality/support of the solution is bounded by a value…

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…

Symmetric submodular maximization is an important class of combinatorial optimization problems, including MAX-CUT on graphs and hyper-graphs. The state-of-the-art algorithm for the problem over general constraints has an approximation ratio…

We study the single-choice Prophet Inequality problem when the gambler is given access to samples. We show that the optimal competitive ratio of $1/2$ can be achieved with a single sample from each distribution. When the distributions are…

In a prophet inequality problem, $n$ independent random variables are presented to a gambler one by one. The gambler decides when to stop the sequence and obtains the most recent value as reward. We evaluate a stopping rule by the…