Related papers: A Parallel Double Greedy Algorithm for Submodular …
Submodular functions -- functions exhibiting diminishing returns -- are central to machine learning. When the objective is monotone and non-negative, the greedy algorithm achieves a tight $63\%$ approximation. But many practical objectives…
Collective communications are ubiquitous in parallel applications. We present two new algorithms for performing a reduction. The operation associated with our reduction needs to be associative and commutative. The two algorithms are…
We consider the problem of stochastic monotone submodular function maximization, subject to constraints. We give results on adaptivity gaps, and on the gap between the optimal offline and online solutions. We present a procedure that…
In this paper we consider a generalization of the well-known budgeted maximum coverage problem. We are given a ground set of elements and a set of bins. The goal is to find a subset of elements along with an associated set of bins, such…
We consider the optimisation problem of adding $k$ links to a given network, such that the resulting effective graph resistance is as small as possible. The problem was recently proven to be NP-hard, such that optimal solutions obtained…
We consider a class of submodular maximization problems in which decision-makers have limited access to the objective function. We explore scenarios where the decision-maker can observe only pairwise information, i.e., can evaluate the…
We propose a new random pruning method (called "submodular sparsification (SS)") to reduce the cost of submodular maximization. The pruning is applied via a "submodularity graph" over the $n$ ground elements, where each directed edge is…
The task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this…
This paper studies the problem of finding an $(1+\epsilon)$-approximate solution to positive semidefinite programs. These are semidefinite programs in which all matrices in the constraints and objective are positive semidefinite and all…
Constrained maximization of submodular functions poses a central problem in combinatorial optimization. In many realistic scenarios, a number of agents need to maximize multiple submodular objectives over the same ground set. We study such…
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…
We study the problem of estimating the size of maximum matching and minimum vertex cover in sublinear time. Denoting the number of vertices by $n$ and the average degree in the graph by $\bar{d}$, we obtain the following results for both…
Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an…
Submodular optimization finds applications in machine learning and data mining. In this paper, we study the problem of maximizing functions of the form $h = f-c$, where $f$ is a monotone, non-negative, weakly submodular set function and $c$…
Motivated by applications in online advertising, we consider a class of maximization problems where the objective is a function of the sequence of actions as well as the running duration of each action. For these problems, we introduce the…
Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…
We study the problem of maximizing a monotone submodular function subject to a matroid independence constraint. For more than a decade, a rich body of work has studied this problem. Initially, a tight approximation of $ (1-\frac{1}{e})$ was…
This paper addresses the task allocation problem for multi-robot systems. The main issue with the task allocation problem is inherent complexity that makes finding an optimal solution within a reasonable time almost impossible. To hand the…
We propose a new concept named adaptive submodularity ratio to study the greedy policy for sequential decision making. While the greedy policy is known to perform well for a wide variety of adaptive stochastic optimization problems in…
The (Non-Preemptive) Throughput Maximization problem is a natural and fundamental scheduling problem. We are given $n$ jobs, where each job $j$ is characterized by a processing time and a time window, contained in a global interval $[0,T)$,…