Related papers: GreedyML: A Parallel Algorithm for Maximizing Cons…
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…
Many large-scale machine learning problems--clustering, non-parametric learning, kernel machines, etc.--require selecting a small yet representative subset from a large dataset. Such problems can often be reduced to maximizing a submodular…
In this paper, we propose a new framework for designing fast parallel algorithms for fundamental statistical subset selection tasks that include feature selection and experimental design. Such tasks are known to be weakly submodular and are…
Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for…
Distributed maximization of a submodular function in the MapReduce (MR) model has received much attention, culminating in two frameworks that allow a centralized algorithm to be run in the MR setting without loss of approximation, as long…
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…
We consider parallel, or low adaptivity, algorithms for submodular function maximization. This line of work was recently initiated by Balkanski and Singer and has already led to several interesting results on the cardinality constraint and…
An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…
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…
We design new serial and parallel approximation algorithms for computing a maximum weight $b$-matching in an edge-weighted graph with a submodular objective function. This problem is NP-hard; the new algorithms have approximation ratio…
We study the problem of maximizing a submodular function, subject to a cardinality constraint, with a set of agents communicating over a connected graph. We propose a distributed greedy algorithm that allows all the agents to converge to a…
We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…
The densest subgraph problem has received significant attention, both in theory and in practice, due to its applications in problems such as community detection, social network analysis, and spam detection. Due to the high cost of obtaining…
It is known that greedy methods perform well for maximizing monotone submodular functions. At the same time, such methods perform poorly in the face of non-monotonicity. In this paper, we show - arguably, surprisingly - that invoking the…
A $k$-submodular function naturally generalizes submodular functions by taking as input $k$ disjoint subsets, rather than a single subset. Unlike standard submodular maximization, which only requires selecting elements for the solution,…
We study the problem of scheduling sensors in a resource-constrained linear dynamical system, where the objective is to select a small subset of sensors from a large network to perform the state estimation task. We formulate this problem as…
Motivated by a wide range of applications in data mining and machine learning, we consider the problem of maximizing a submodular function subject to supermodular cost constraints. In contrast to the well-understood setting of cardinality…
The problem of column subset selection has recently attracted a large body of research, with feature selection serving as one obvious and important application. Among the techniques that have been applied to solve this problem, the greedy…
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…
Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the…