Related papers: A Greedy Strategy for Graph Cut

We consider a class of discrete optimization problems that aim to maximize a submodular objective function subject to a distributed partition matroid constraint. More precisely, we consider a networked scenario in which multiple agents…

The submodular maximization problem is widely applicable in many engineering problems where objectives exhibit diminishing returns. While this problem is known to be NP-hard for certain subclasses of objective functions, there is a greedy…

Graph partitioning is one of an important set of well-known compute-intense (NP-hard) graph problems that devolve to discrete constrained optimization. We sampled solutions to the problem via two different quantum-ready methods to…

The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…

The "classical" (weak) greedy algorithm is widely used within model order reduction in order to compute a reduced basis in the offline training phase: An a posteriori error estimator is maximized and the snapshot corresponding to the…

We consider parametrized linear-quadratic optimal control problems and provide their online-efficient solutions by combining greedy reduced basis methods and machine learning algorithms. To this end, we first extend the greedy control…

Clustering points in a vector space or nodes in a graph is a ubiquitous primitive in statistical data analysis, and it is commonly used for exploratory data analysis. In practice, it is often of interest to "refine" or "improve" a given…

Graph Neural Networks (GNNs) tend to suffer from high computation costs due to the exponentially increasing scale of graph data and the number of model parameters, which restricts their utility in practical applications. To this end, some…

Linear reversible circuits represent a subclass of reversible circuits with many applications in quantum computing. These circuits can be efficiently simulated by classical computers and their size is polynomially bounded by the number of…

This article empirically examines the computational cost of solving a known hard problem, graph clustering, using novel purpose-built computer hardware. We express the graph clustering problem as an intra-cluster distance or dissimilarity…

Finding dense subgraphs of a large graph is a standard problem in graph mining that has been studied extensively both for its theoretical richness and its many practical applications. In this paper we introduce a new family of dense…

Despite plentiful successes achieved by graph representation learning in various domains, the training of graph neural networks (GNNs) still remains tenaciously challenging due to the tremendous computational overhead needed for sizable…

In mixed-integer programming (MIP) solvers, cutting planes are essential for Branch-and-Cut (B&C) algorithms as they reduce the search space and accelerate the solving process. Traditional methods rely on hard-coded heuristics for cut plane…

Here we study the problem of matched record clustering in unsupervised entity resolution. We build upon a state-of-the-art probabilistic framework named the Data Washing Machine (DWM). We introduce a graph-based hierarchical 2-step record…

We propose a new algorithm for solving the graph-fused lasso (GFL), a method for parameter estimation that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. Our key insight is to…

We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut…

Structural parameters of graph (such as degeneracy and arboricity) had rarely been considered when designing algorithms for $\textit{(edge) clique cover}$ problems. Taking degeneracy of graph into account, we present a greedy framework and…

Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…

Randomized Greedy Algorithms (RGAs) are interesting approaches to solve problems whose structures are not well understood as well as problems in combinatorial optimization which incorporate the random processes and the greedy algorithms.…

Spectral clustering (SC) and graph-based semi-supervised learning (SSL) algorithms are sensitive to how graphs are constructed from data. In particular if the data has proximal and unbalanced clusters these algorithms can lead to poor…