Related papers: Submodular Matroid Secretary Problem with Shortlis…
In an instance of the minimum eigenvalue problem, we are given a collection of $n$ vectors $v_1,\ldots, v_n \subset {\mathbb{R}^d}$, and the goal is to pick a subset $B\subseteq [n]$ of given vectors to maximize the minimum eigenvalue of…
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…
We study the canonical problem of maximizing a stochastic submodular function subject to a cardinality constraint, where the goal is to select a subset from a ground set of items with uncertain individual performances to maximize their…
We study the classic set cover problem from the perspective of sub-linear algorithms. Given access to a collection of $m$ sets over $n$ elements in the query model, we show that sub-linear algorithms derived from existing techniques have…
In this paper, we consider the unconstrained submodular maximization problem. We propose the first algorithm for this problem that achieves a tight $(1/2-\varepsilon)$-approximation guarantee using $\tilde{O}(\varepsilon^{-1})$ adaptive…
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…
We introduce and study the problem of consistent low-rank approximation, in which rows of an input matrix $\mathbf{A}\in\mathbb{R}^{n\times d}$ arrive sequentially and the goal is to provide a sequence of subspaces that well-approximate the…
In this paper we study the adaptivity of submodular maximization. Adaptivity quantifies the number of sequential rounds that an algorithm makes when function evaluations can be executed in parallel. Adaptivity is a fundamental concept that…
Top-K queries are an established heuristic in information retrieval. This paper presents an approach for optimal tiered storage allocation under stream processing workloads using this heuristic: those requiring the analysis of only the…
Submodular maximization arises in many applications, and has attracted a lot of research attentions from various areas such as artificial intelligence, finance and operations research. Previous studies mainly consider only one kind of…
Many important problems in discrete optimization require maximization of a monotonic submodular function subject to matroid constraints. For these problems, a simple greedy algorithm is guaranteed to obtain near-optimal solutions. In this…
A matroid is a notion of independence in combinatorial optimization which is closely related to computational efficiency. In particular, it is well known that the maximum of a constrained modular function can be found greedily if and only…
In the submodular ranking (SR) problem, the input consists of a set of submodular functions defined on a ground set of elements. The goal is to order elements for all the functions to have value above a certain threshold as soon on average…
We present a simple combinatorial $\frac{1 -e^{-2}}{2}$-approximation algorithm for maximizing a monotone submodular function subject to a knapsack and a matroid constraint. This classic problem is known to be hard to approximate within…
Maximizing monotone submodular functions under cardinality constraints is a classic optimization task with several applications in data mining and machine learning. In this paper we study this problem in a dynamic environment with…
We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order.…
We initiate a broad study of classical problems in the streaming model with insertions and deletions in the setting where we allow the approximation factor $\alpha$ to be much larger than $1$. Such algorithms can use significantly less…
In this paper, we study the problem of finding a maximum matching in the semi-streaming model when edges arrive in a random order. In the semi-streaming model, an algorithm receives a stream of edges and it is allowed to have a memory of…
We consider generalizations of the classical secretary problem, also known as the problem of optimal choice, to posets where the only information we have is the size of the poset and the number of maximal elements. We show that, given this…
Constrained submodular maximization problems encompass a wide variety of applications, including personalized recommendation, team formation, and revenue maximization via viral marketing. The massive instances occurring in modern day…