Related papers: A General Coreset-Based Approach to Diversity Maxi…
A natural way to deal with multiple, partially conflicting objectives is turning all the objectives but one into budget constraints. Some classical polynomial-time optimization problems, such as spanning tree and forest, shortest path,…
Submodular function maximization is a central problem in combinatorial optimization, generalizing many important problems including Max Cut in directed/undirected graphs and in hypergraphs, certain constraint satisfaction problems, maximum…
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. Some of the most…
In this paper, we present a general framework for efficiently computing diverse solutions to combinatorial optimization problems. Given a problem instance, the goal is to find $k$ solutions that maximize a specified diversity measure; the…
Analytical theories suggest that higher-quality data can lead to lower test errors in models trained on a fixed data budget. Moreover, a model can be trained on a lower compute budget without compromising performance if a dataset can be…
We introduce a new iterative rounding technique to round a point in a matroid polytope subject to further matroid constraints. This technique returns an independent set in one matroid with limited violations of the other ones. On top of the…
We present a novel coreset construction algorithm for solving classification tasks using Support Vector Machines (SVMs) in a computationally efficient manner. A coreset is a weighted subset of the original data points that provably…
Coreset selection compresses large datasets into compact, representative subsets, reducing the energy and computational burden of training deep neural networks. Existing methods are either: (i) DNN-based, which are tied to model-specific…
Subsampling algorithms are a natural approach to reduce data size before fitting models on massive datasets. In recent years, several works have proposed methods for subsampling rows from a data matrix while maintaining relevant information…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
Given two matroids $\mathcal{M}_1$ and $\mathcal{M}_2$ over the same $n$-element ground set, the matroid intersection problem is to find a largest common independent set, whose size we denote by $r$. We present a simple and generic auction…
We study the problem of maximizing a monotone submodular function subject to a matroid constraint, and present for it a deterministic non-oblivious local search algorithm that has an approximation guarantee of $1 - 1/e - \varepsilon$ (for…
Given a set of points in a metric space, the $(k,z)$-clustering problem consists of finding a set of $k$ points called centers, such that the sum of distances raised to the power of $z$ of every data point to its closest center is…
We study the robust geometric median problem in Euclidean space $\mathbb{R}^d$, with a focus on coreset construction.A coreset is a compact summary of a dataset $P$ of size $n$ that approximates the robust cost for all centers $c$ within a…
Given two matroids $\mathcal{M}_1$ and $\mathcal{M}_2$ over the same ground set, the matroid intersection problem is to find the maximum cardinality common independent set. In the weighted version of the problem, the goal is to find a…
A coreset (or core-set) of an input set is its small summation, such that solving a problem on the coreset as its input, provably yields the same result as solving the same problem on the original (full) set, for a given family of problems…
Designing a search heuristic for constraint programming that is reliable across problem domains has been an important research topic in recent years. This paper concentrates on one family of candidates: counting-based search. Such…
We study the online submodular maximization problem with free disposal under a matroid constraint. Elements from some ground set arrive one by one in rounds, and the algorithm maintains a feasible set that is independent in the underlying…
We introduce the parametric matroid one-interdiction problem. Given a matroid, each element of its ground set is associated with a weight that depends linearly on a real parameter from a given parameter interval. The goal is to find, for…
Much energy has been devoted to developing a matroid's computational properties, yet parallel algorithm design for matroid optimization seems less understood. Specifically, the current state of the art is a folklore reduction from…