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The standard greedy algorithm has been recently shown to enjoy approximation guarantees for constrained non-submodular nondecreasing set function maximization. While these recent results allow to better characterize the empirical success of…
Submodular functions are a broad class of set functions, which naturally arise in diverse areas. Many algorithms have been suggested for the maximization of these functions. Unfortunately, once the function deviates from submodularity, the…
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…
The submodular maximization problem is widely applicable in many engineering problems where objectives exhibit diminishing returns. While this problem is known to be NP-hard for certain subclasses of objective functions, there is a greedy…
The outbreak of a pandemic, such as COVID-19, causes major health crises worldwide. Typical measures to contain the rapid spread usually include effective vaccination and strict interventions (Nature Human Behaviour, 2021). Motivated by…
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…
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…
The general problem in this paper is vertex (node) subset selection with the goal to contain an infection that spreads in a network. Instead of selecting the single most important node, this paper deals with the problem of selecting…
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…
Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…
In this paper, we study streaming and online algorithms in the context of randomness in the input. For several problems, a random order of the input sequence---as opposed to the worst-case order---appears to be a necessary evil in order to…
Submodular optimization is a special class of combinatorial optimization arising in several machine learning problems, but also in cooperative control of complex systems. In this paper, we consider agents in an asynchronous, unreliable and…
This paper considers the problem of designing non-pharmaceutical intervention (NPI) strategies, such as masking and social distancing, to slow the spread of a viral epidemic. We formulate the problem of jointly minimizing the infection…
Submodularity in combinatorial optimization has been a topic of many studies and various algorithmic techniques exploiting submodularity of a studied problem have been proposed. It is therefore natural to ask, in cases where the cost…
A topic propagating in a social network reaches its tipping point if the number of users discussing it in the network exceeds a critical threshold such that a wide cascade on the topic is likely to occur. In this paper, we consider the task…
We consider a class of discrete optimization problems that aim to maximize a submodular objective function subject to a distributed partition matroid constraint. More precisely, we consider a networked scenario in which multiple agents…
Targeted immunization or attacks of large-scale networks has attracted significant attention by the scientific community. However, in real-world scenarios, knowledge and observations of the network may be limited thereby precluding a full…
Most communication networks are complex. In this paper, we address one of the fundamental problems we are facing nowadays, namely, how we can efficiently protect these networks. To this end, we study an immunization strategy and found that…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
We introduce an immunization method where the percentage of required vaccinations for immunity are close to the optimal value of a targeted immunization scheme of highest degree nodes. Our strategy retains the advantage of being purely…