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Matching is one of the most fundamental and broadly applicable problems across many domains. In these diverse real-world applications, there is often a degree of uncertainty in the input which has led to the study of stochastic matching…
We describe a parallel approximation algorithm for maximizing monotone submodular functions subject to hereditary constraints on distributed memory multiprocessors. Our work is motivated by the need to solve submodular optimization problems…
Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained…
Setcover greedy algorithm is a natural approximation algorithm for test set problem. This paper gives a precise and tighter analysis of performance guarantee of this algorithm. The author improves the performance guarantee $2\ln n$ which…
We study the problem of maximizing a monotone submodular function subject to a matroid constraint, and present for it a deterministic non-oblivious local search algorithm that has an approximation guarantee of $1 - 1/e - \varepsilon$ (for…
We briefly discuss the greedy method and a couple of its more efficient variants for approximately maximizing monotone submodular functions.
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…
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 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 study the problem of maximizing a non-monotone, non-negative submodular function subject to a matroid constraint. The prior best-known deterministic approximation ratio for this problem is $\frac{1}{4}-\epsilon$ under…
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…
In this work we present the first practical $\left(\frac{1}{e}-\epsilon\right)$-approximation algorithm to maximise a general non-negative submodular function subject to a matroid constraint. Our algorithm is based on combining the…
In this work, we study the Stochastic Budgeted Multi-round Submodular Maximization (SBMSm) problem, where we aim to adaptively maximize the sum, over multiple rounds, of a monotone and submodular objective function defined on subsets of…
We study dynamic algorithms for the problem of maximizing a monotone submodular function over a stream of $n$ insertions and deletions. We show that any algorithm that maintains a $(0.5+\epsilon)$-approximate solution under a cardinality…
We introduce the problem of maximizing approximately $k$-submodular functions subject to size constraints. In this problem, one seeks to select $k$-disjoint subsets of a ground set with bounded total size or individual sizes, and maximum…
In this paper we prove the efficacy of a simple greedy algorithm for a finite horizon online resource allocation/matching problem, when the corresponding static planning linear program (SPP) exhibits a non-degeneracy condition called the…
We generalize the problem of online submodular welfare maximization to incorporate various stochastic elements that have gained significant attention in recent years. We show that a non-adaptive Greedy algorithm, which is oblivious to the…
This work provides performance guarantees for the greedy solution of experimental design problems. In particular, it focuses on A- and E-optimal designs, for which typical guarantees do not apply since the mean-square error and the maximum…
Submodular function maximization is a central problem in combinatorial optimization, generalizing many important problems including Max Cut in directed/undirected graphs and in hypergraphs, certain constraint satisfaction problems, maximum…
Maximizing submodular functions under cardinality constraints lies at the core of numerous data mining and machine learning applications, including data diversification, data summarization, and coverage problems. In this work, we study this…