Related papers: A Tight Bound for Stochastic Submodular Cover

We consider the classic Set Cover problem in the data stream model. For $n$ elements and $m$ sets ($m\geq n$) we give a $O(1/\delta)$-pass algorithm with a strongly sub-linear $\tilde{O}(mn^{\delta})$ space and logarithmic approximation…

For many optimization problems in machine learning, finding an optimal solution is computationally intractable and we seek algorithms that perform well in practice. Since computational intractability often results from pathological…

Greedy bases are those bases where the Thresholding Greedy Algorithm (introduced by S. V. Konyagin and V. N. Temlyakov) produces the best possible approximation up to a constant. In 2017, Bern\'a and Blasco gave a characterization of these…

We consider a problem of maximizing a monotone DR-submodular function under multiple order-consistent knapsack constraints on a distributive lattice. Since a distributive lattice is used to represent a dependency constraint, the problem can…

Kernel interpolation is a versatile tool for the approximation of functions from data, and it can be proven to have some optimality properties when used with kernels related to certain Sobolev spaces. In the context of interpolation, the…

We introduce a natural generalization of submodular set cover and exact active learning with a finite hypothesis class (query learning). We call this new problem interactive submodular set cover. Applications include advertising in social…

We study partial and budgeted versions of the well studied connected dominating set problem. In the partial connected dominating set problem, we are given an undirected graph G = (V,E) and an integer n', and the goal is to find a minimum…

Control scheduling refers to the problem of assigning agents or actuators to act upon a dynamical system at specific times so as to minimize a quadratic control cost, such as the objective of the Linear-quadratic-Gaussian (LQG) or the…

We consider interactive learning and covering problems, in a setting where actions may incur different costs, depending on the response to the action. We propose a natural greedy algorithm for response-dependent costs. We bound the…

In this paper, we consider the optimization problem Submodular Cover (SCP), which is to find a minimum cardinality subset of a finite universe $U$ such that the value of a submodular function $f$ is above an input threshold $\tau$. In…

In this article we prove that the minimum-degree greedy algorithm, with adversarial tie-breaking, is a $(2/3)$-approximation for the Maximum Independent Set problem on interval graphs. We show that this is tight, even on unit interval…

The greedy algorithm adapted from Kruskal's algorithm is an efficient and folklore way to produce a $k$-spanner with girth at least $k+2$. The greedy algorithm has shown to be `existentially optimal', while it's not `universally optimal'…

We consider the problem of covering multiple submodular constraints. Given a finite ground set $N$, a cost function $c: N \rightarrow \mathbb{R}_+$, $r$ monotone submodular functions $f_1,f_2,\ldots,f_r$ over $N$ and requirements…

Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for…

An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…

We provide new approximation guarantees for greedy low rank matrix estimation under standard assumptions of restricted strong convexity and smoothness. Our novel analysis also uncovers previously unknown connections between the low rank…

The Set Cover problem (SCP) and Set Packing problem (SPP) are standard NP-hard combinatorial optimization problems. Their decision problem versions are shown to be NP-Complete in Karp's 1972 paper. We specify a rough guide to constructing…

Submodular maximization under matroid constraints is a fundamental problem in combinatorial optimization with applications in sensing, data summarization, active learning, and resource allocation. While the Sequential Greedy (SG) algorithm…

The problem of selecting a small-size representative summary of a large dataset is a cornerstone of machine learning, optimization and data science. Motivated by applications to recommendation systems and other scenarios with query-limited…

We study the maximum capture problem in facility location under random utility models, i.e., the problem of seeking to locate new facilities in a competitive market such that the captured user demand is maximized, assuming that each…