Related papers: Performance guarantees for greedy maximization of …
We investigate the performance of the standard Greedy algorithm for cardinality constrained maximization of non-submodular nondecreasing set functions. While there are strong theoretical guarantees on the performance of Greedy for…
This letter studies the problem of minimizing increasing set functions, or equivalently, maximizing decreasing set functions, over the base of a matroid. This setting has received great interest, since it generalizes several applied…
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…
We study a linear quadratic regulation problem with a constraint where the control input can be nonzero only at a limited number of times. Given that this constraint leads to a combinational optimization problem, we adopt a greedy method to…
We present new tight performance guarantees for the greedy maximization of nondecreasing submodular set functions. Our main result first provides a performance guarantee in terms of the overlap of the optimal and greedy solutions. As a…
We consider a class of multi-agent optimal coverage problems in which the goal is to determine the optimal placement of a group of agents in a given mission space so that they maximize a coverage objective that represents a blend of…
Controllability and observability have long been recognized as fundamental structural properties of dynamical systems, but have recently seen renewed interest in the context of large, complex networks of dynamical systems. A basic problem…
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…
Submodular functions -- functions exhibiting diminishing returns -- are central to machine learning. When the objective is monotone and non-negative, the greedy algorithm achieves a tight $63\%$ approximation. But many practical objectives…
The quantification of controllability and observability has recently received new interest in the context of large, complex networks of dynamical systems. A fundamental but computationally difficult problem is the placement or selection of…
We propose and analyze batch greedy heuristics for cardinality constrained maximization of non-submodular non-decreasing set functions. We consider the standard greedy paradigm, along with its distributed greedy and stochastic greedy…
We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the…
With the rising importance of large-scale network control, the problem of actuator placement has received increasing attention. Our goal in this paper is to find a set of actuators minimizing the metric that measures the average energy…
We consider the optimal coverage problem where a multi-agent network is deployed in an environment with obstacles to maximize a joint event detection probability. The objective function of this problem is non-convex and no global optimum is…
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 classical problem of maximizing a submodular function under a matroid constraint is considered. Defining a new measure for the increments made by the greedy algorithm at each step, called the discriminant, improved approximation ratio…
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…
Weak submodularity is a natural relaxation of the diminishing return property, which is equivalent to submodularity. Weak submodularity has been used to show that many (monotone) functions that arise in practice can be efficiently maximized…
Utilizing the capabilities of configurable sensing systems requires addressing difficult information gathering problems. Near-optimal approaches exist for sensing systems without internal states. However, when it comes to optimizing the…
We consider the problem of maximizing non-negative non-decreasing set functions. Although most of the recent work focus on exploiting submodularity, it turns out that several objectives we encounter in practice are not submodular.…