Related papers: An Approximation Algorithm for a General Class of …
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
We consider two well-known natural variants of bin packing, and show that these packing problems admit asymptotic fully polynomial time approximation schemes (AFPTAS). In bin packing problems, a set of one-dimensional items of size at most…
A multiple knapsack constraint over a set of items is defined by a set of bins of arbitrary capacities, and a weight for each of the items. An assignment for the constraint is an allocation of subsets of items to the bins which adheres to…
Many problems are NP-hard and, unless P = NP, do not admit polynomial-time exact algorithms. The fastest known exact algorithms exactly usually take time exponential in the input size. Much research effort has gone into obtaining faster…
We consider a recently introduced fair repetitive scheduling problem involving a set of clients, each asking for their associated job to be daily scheduled on a single machine across a finite planning horizon. The goal is to determine a job…
In this paper, we study the non-bipartite maximum matching problem in the semi-streaming model. The maximum matching problem in the semi-streaming model has received a significant amount of attention lately. While the problem has been…
In the Maximum Independent Set of Objects problem, we are given an $n$-vertex planar graph $G$ and a family $\mathcal{D}$ of $N$ objects, where each object is a connected subgraph of $G$. The task is to find a subfamily $\mathcal{F}…
The subject of this paper is the time complexity of approximating Knapsack, Subset Sum, Partition, and some other related problems. The main result is an $\widetilde{O}(n+1/\varepsilon^{5/3})$ time randomized FPTAS for Partition, which is…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…
We give an $\alpha(1+\epsilon)$-approximation algorithm for solving covering LPs, assuming the presence of a $(1/\alpha)$-approximation algorithm for a certain optimization problem. Our algorithm is based on a simple modification of the…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
In multi-criteria optimization problems, several objective functions have to be optimized. Since the different objective functions are usually in conflict with each other, one cannot consider only one particular solution as the optimal…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
In real-time systems, in addition to the functional correctness recurrent tasks must fulfill timing constraints to ensure the correct behavior of the system. Partitioned scheduling is widely used in real-time systems, i.e., the tasks are…
In many submodular optimization applications, datasets are naturally partitioned into disjoint subsets. These scenarios give rise to submodular optimization problems with partition-based constraints, where the desired solution set should be…
In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…
We study the two-dimensional (geometric) knapsack problem with rotations (2DKR), in which we are given a square knapsack and a set of rectangles with associated profits. The objective is to find a maximum profit subset of rectangles that…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
We consider the Low Rank Approximation problem, where the input consists of a matrix $A \in \mathbb{R}^{n_R \times n_C}$ and an integer $k$, and the goal is to find a matrix $B$ of rank at most $k$ that minimizes $\| A - B \|_0$, which is…
We consider the stochastic geometry model where the location of each node is a random point in a given metric space, or the existence of each node is uncertain. We study the problems of computing the expected lengths of several…