Related papers: FPT Approximation Schemes for Maximizing Submodula…
We develop approximation algorithms for set-selection problems with deterministic constraints, but random objective values, i.e., stochastic probing problems. When the goal is to maximize the objective, approximation algorithms for probing…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
We study the problem of selecting a subset of k random variables from a large set, in order to obtain the best linear prediction of another variable of interest. This problem can be viewed in the context of both feature selection and sparse…
Given a finite number of samples of a continuous set-valued function F, mapping an interval to non-empty compact subsets of $\mathbb{R}^d$, $F: [a,b] \to K(\mathbb{R}^d)$, we discuss the problem of computing good approximations of F. We…
Maximization of {\it non-submodular} functions appears in various scenarios, and many previous works studied it based on some measures that quantify the closeness to being submodular. On the other hand, many practical non-submodular…
The goal of a typical adaptive sequential decision making problem is to design an interactive policy that selects a group of items sequentially, based on some partial observations, to maximize the expected utility. It has been shown that…
Submodular function maximization finds application in a variety of real-world decision-making problems. However, most existing methods, based on greedy maximization, assume it is computationally feasible to evaluate F, the function being…
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…
(see paper for full abstract) Cut problems and connectivity problems on digraphs are two well-studied classes of problems from the viewpoint of parameterized complexity. After a series of papers over the last decade, we now have (almost)…
In this work, we consider the maximization of submodular functions constrained by independence systems. Because of the wide applicability of submodular functions, this problem has been extensively studied in the literature, on specialized…
In the classical selection problem, the input consists of a collection of elements and the goal is to pick a subset of elements from the collection such that some objective function $f$ is maximized. This problem has been studied…
We analyze the performance of the greedy algorithm, and also a discrete semi-gradient based algorithm, for maximizing the sum of a suBmodular and suPermodular (BP) function (both of which are non-negative monotone non-decreasing) under two…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
Submodular Functions are a special class of set functions, which generalize several information-theoretic quantities such as entropy and mutual information [1]. Submodular functions have subgradients and subdifferentials [2] and admit…
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…
Submodular function maximization is a fundamental combinatorial optimization problem with plenty of applications -- including data summarization, influence maximization, and recommendation. In many of these problems, the goal is to find a…
We study the problem of differentially private constrained maximization of decomposable submodular functions. A submodular function is decomposable if it takes the form of a sum of submodular functions. The special case of maximizing a…
We propose and discuss a new computational method for the numerical approximation of reachable sets for nonlinear control systems. It is based on the support vector machine algorithm and represents the set approximation as a sublevel set of…
Submodular functions allow to model many real-world optimisation problems. This paper introduces approaches for computing diverse sets of high quality solutions for submodular optimisation problems. We first present diversifying greedy…
In recent years we have witnessed an increase on the development of methods for submodular optimization, which have been motivated by the wide applicability of submodular functions in real-world data-science problems. In this paper, we…