Related papers: Efficient Branch-and-Bound for Submodular Function…
This work, for the first time, introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular maximization over a ground set of size $n$ subject to a knapsack constraint, $\mathsf{DLA}$ and…
We study the correlated stochastic knapsack problem of a submodular target function, with optional additional constraints. We utilize the multilinear extension of submodular function, and bundle it with an adaptation of the relaxed linear…
Clustering with submodular functions has been of interest over the last few years. Symmetric submodular functions are of particular interest as minimizing them is significantly more efficient and they include many commonly used functions in…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
Stochastic knapsack problem originally was a versatile model for controls in telecommunication networks. Recently, it draws attentions of revenue management community by serving as a basic model for allocating resources over time. We…
We present a branch-and-bound algorithm for globally solving parabolic optimal control problems with binary switches that have bounded variation and possibly need to satisfy further combinatorial constraints. More precisely, for a given…
The problem of maximizing a constrained monotone set function has many practical applications and generalizes many combinatorial problems. Unfortunately, it is generally not possible to maximize a monotone set function up to an acceptable…
We study a robust extensible bin packing problem with budgeted uncertainty, under a budgeted uncertainty model where item sizes are defined to lie in the intersection of a box with a one-norm ball. We propose a scenario generation algorithm…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
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…
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…
Maximizing a non-negative, monontone, submodular function $f$ over $n$ elements under a cardinality constraint $k$ (SMCC) is a well-studied NP-hard problem. It has important applications in, e.g., machine learning and influence…
Multi-armed bandit problems are the predominant theoretical model of exploration-exploitation tradeoffs in learning, and they have countless applications ranging from medical trials, to communication networks, to Web search and advertising.…
Packing problems are an important class of optimization problems. The probably most well-known problem if this type is knapsack and many generalizations of it have been studied in the literature like Two-dimensional Geometric Knapsack…
In this paper we design a new primal-dual algorithm for the classic discrete optimization problem of maximizing a monotone submodular function subject to a cardinality constraint achieving the optimal approximation of $(1-1/e)$. This…
We present a new approach for studying the problem of optimal hedging of a European option in a finite and complete discrete-time market model. We consider partial hedging strategies that maximize the success probability or minimize the…
The multiple knapsack problem with grouped items aims to maximize rewards by assigning groups of items among multiple knapsacks, considering knapsack capacities. Either all items in a group are assigned or none at all. We propose algorithms…
We consider the problem of maximizing submodular functions; while this problem is known to be NP-hard, several numerically efficient local search techniques with approximation guarantees are available. In this paper, we propose a novel…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
We study the Min-Weighted Sum Bin Packing problem, a variant of the classical Bin Packing problem in which items have a weight, and each item induces a cost equal to its weight multiplied by the index of the bin in which it is packed. This…