Related papers: Efficient Algorithms for Monotone Non-Submodular M…
We study the problem of maximizing a monotone submodular function with viability constraints. This problem originates from computational biology, where we are given a phylogenetic tree over a set of species and a directed graph, the…
We consider a problem of optimizing convex functionals over matroid bases. It is richly expressive and captures certain quadratic assignment and clustering problems. While generally NP-hard, we show it is polynomial time solvable when a…
We study submodular maximization problems with matroid constraints, in particular, problems where the objective can be expressed via compositions of analytic and multilinear functions. We show that for functions of this form, the so-called…
We study the problem of maximizing a stochastic monotone submodular function with respect to a matroid constraint. Due to the presence of diminishing marginal values in real-world problems, our model can capture the effect of stochasticity…
For constrained, not necessarily monotone submodular maximization, all known approximation algorithms with ratio greater than $1/e$ require continuous ideas, such as queries to the multilinear extension of a submodular function and its…
We study the problem of maximizing a monotone submodular function subject to a matroid constraint and present a deterministic algorithm that achieves (1/2 + {\epsilon})-approximation for the problem. This algorithm is the first…
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…
Migration presents sweeping societal challenges that have recently attracted significant attention from the scientific community. One of the prominent approaches that have been suggested employs optimization and machine learning to match…
Maximizing a single submodular set function subject to a cardinality constraint is a well-studied and central topic in combinatorial optimization. However, finding a set that maximizes multiple functions at the same time is much less…
The problem of maximizing non-negative monotone submodular functions under a certain constraint has been intensively studied in the last decade. In this paper, we address the problem for functions defined over the integer lattice. Suppose…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
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…
We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous…
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…
We consider the problem of monotone, submodular maximization over a ground set of size $n$ subject to cardinality constraint $k$. For this problem, we introduce the first deterministic algorithms with linear time complexity; these…
We establish the optimal nonergodic sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems. First, the optimal bound is formulated by the performance estimation framework, resulting in an infinite…
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 extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…
Multi-task learning has gained popularity due to the advantages it provides with respect to resource usage and performance. Nonetheless, the joint optimization of parameters with respect to multiple tasks remains an active research topic.…
Maximizing a monotone submodular function under cardinality constraint $k$ is a core problem in machine learning and database with many basic applications, including video and data summarization, recommendation systems, feature extraction,…