Related papers: Greedy algorithms for high-dimensional eigenvalue …
Considering the set cover problem, by modifying the approach that gives a logarithmic approximation guarantee for the greedy algorithm, we obtain an estimation of the greedy algorithm's accuracy for a particular input. We compare the…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
We propose a greedy algorithm to select $N$ important features among $P$ input features for a non-linear prediction problem. The features are selected one by one sequentially, in an iterative loss minimization procedure. We use neural…
In this article we prove that the minimum-degree greedy algorithm, with adversarial tie-breaking, is a $(2/3)$-approximation for the Maximum Independent Set problem on interval graphs. We show that this is tight, even on unit interval…
Optimal experimental design (OED) concerns itself with identifying ideal methods of data collection, e.g.~via sensor placement. The \emph{greedy algorithm}, that is, placing one sensor at a time, in an iteratively optimal manner, stands as…
We revisit the classical problem of optimal experimental design (OED) under a new mathematical model grounded in a geometric motivation. Specifically, we introduce models based on elementary symmetric polynomials; these polynomials capture…
The aim of this paper is to develop an algebraic multigrid method to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. Our approach uses the…
The contextual bandit literature has traditionally focused on algorithms that address the exploration-exploitation tradeoff. In particular, greedy algorithms that exploit current estimates without any exploration may be sub-optimal in…
Solving stochastic optimization problems under partial observability, where one needs to adaptively make decisions with uncertain outcomes, is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of…
Given a Banach space X and one of its compact sets F, we consider the problem of finding a good n dimensional space X_n \subset X which can be used to approximate the elements of F. The best possible error we can achieve for such an…
We propose a new greedy algorithm for the maximum cardinality matching problem. We give experimental evidence that this algorithm is likely to find a maximum matching in random graphs with constant expected degree c>0, independent of the…
A vector-measurement-sensor problem for the least squares estimation is considered, by extending a previous novel approach in this paper. An extension of the vector-measurement-sensor selection of the greedy algorithm is proposed and is…
Distributed optimization is pivotal for large-scale signal processing and machine learning, yet communication overhead remains a major bottleneck. Low-rank gradient compression, in which the transmitted gradients are approximated by…
Cost-efficient compressive sensing is challenging when facing large-scale data, {\em i.e.}, data with large sizes. Conventional compressive sensing methods for large-scale data will suffer from low computational efficiency and massive…
MAXCUT defines a classical NP-hard problem for graph partitioning and it serves as a typical case of the symmetric non-monotone Unconstrained Submodular Maximization (USM) problem. Applications of MAXCUT are abundant in machine learning,…
More precise estimation of the greedy algorithm complexity for a special case of the set cover problem is given in this paper.
Motivated by applications in online dating and kidney exchange, the stochastic matching problem was introduced by Chen, Immorlica, Karlin, Mahdian and Rudra (2009). They have proven a 4-approximation of a simple greedy strategy, but…
We consider a class of distributed submodular maximization problems in which each agent must choose a single strategy from its strategy set. The global objective is to maximize a submodular function of the strategies chosen by each agent.…
The realization that selfish interests need to be accounted for in the design of algorithms has produced many contributions in computer science under the umbrella of algorithmic mechanism design. Novel algorithmic properties and paradigms…
Eigenvectors of matrices on a network have been used for understanding spectral clustering and influence of a vertex. For matrices with small geodesic-width, we propose a distributed iterative algorithm in this letter to find eigenvectors…