Related papers: An Approximation Algorithm for a General Class of …
We give a number of approximation metatheorems for monotone maximization problems expressible in the first-order logic, in substantially more general settings than the previously known. We obtain * constant-factor approximation algorithm in…
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…
The seminar assignment problem is a variant of the generalized assignment problem in which items have unit size and the amount of space allowed in each bin is restricted to an arbitrary set of values. The problem has been shown to be…
We develop simple and general techniques to obtain faster (near-linear time) static approximation algorithms, as well as efficient dynamic data structures, for four fundamental geometric optimization problems: minimum piercing set (MPS),…
We generalize the fractional packing framework of Garg and Koenemann to the case of linear fractional packing problems over polyhedral cones. More precisely, we provide approximation algorithms for problems of the form $\max\{c^T x : Ax…
Submodular optimization generalizes many classic problems in combinatorial optimization and has recently found a wide range of applications in machine learning (e.g., feature engineering and active learning). For many large-scale…
This paper presents an algorithm for solving multiobjective optimization problems involving composite functions, where we minimize a quadratic model that approximates $F(x) - F(x^k)$ and that can be derivative-free. We establish theoretical…
This paper studies the maximum cardinality matching problem in stochastically evolving graphs. We formally define the arrival-departure model with stochastic departures. There, a graph is sampled from a specific probability distribution and…
Motivated by applications in machine learning, such as subset selection and data summarization, we consider the problem of maximizing a monotone submodular function subject to mixed packing and covering constraints. We present a tight…
We give an asymptotic approximation scheme (APTAS) for the problem of packing a set of circles into a minimum number of unit square bins. To obtain rational solutions, we use augmented bins of height $1+\gamma$, for some arbitrarily small…
Non-monotone constrained submodular maximization plays a crucial role in various machine learning applications. However, existing algorithms often struggle with a trade-off between approximation guarantees and practical efficiency. The…
In this paper, we propose a general class of algorithms for optimizing an extensive variety of nonsmoothly penalized objective functions that satisfy certain regularity conditions. The proposed framework utilizes the…
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…
Maximum consensus estimation plays a critically important role in robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify…
Given $n$ independent random variables $X_1, X_2, ..., X_n$ and an integer $C$, we study the fundamental problem of computing the probability that the sum $X=X_1+X_2+...+X_n$ is at most $C$. We assume that each random variable $X_i$ is…
In the moldable job scheduling problem one has to assign a set of $n$ jobs to $m$ machines, in order to minimize the time it takes to process all jobs. Each job is moldable, so it can be assigned not only to one but any number of the equal…
Counting the independent sets of a graph is a classical #P-complete problem, even in the bipartite case. We give an exponential-time approximation scheme for this problem which is faster than the best known algorithm for the exact problem.…
We study the optimization version of constraint satisfaction problems (Max-CSPs) in the framework of parameterized complexity; the goal is to compute the maximum fraction of constraints that can be satisfied simultaneously. In standard…
We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…
Constrained submodular maximization problems encompass a wide variety of applications, including personalized recommendation, team formation, and revenue maximization via viral marketing. The massive instances occurring in modern day…