Related papers: On Greedy Approaches to Hierarchical Aggregation
In large datasets, it is hard to discover and analyze structure. It is thus common to introduce tags or keywords for the items. In applications, such datasets are then filtered based on these tags. Still, even medium-sized datasets with a…
Recently, neural networks have been widely applied for solving partial differential equations (PDEs). Although such methods have been proven remarkably successful on practical engineering problems, they have not been shown, theoretically or…
Clustering a graph means identifying internally dense subgraphs which are only sparsely interconnected. Formalizations of this notion lead to measures that quantify the quality of a clustering and to algorithms that actually find…
We study the balanced $k$-way hypergraph partitioning problem, with a special focus on its practical applications to manycore scheduling. Given a hypergraph on $n$ nodes, our goal is to partition the node set into $k$ parts of size at most…
Motivated by a wide range of applications in data mining and machine learning, we consider the problem of maximizing a submodular function subject to supermodular cost constraints. In contrast to the well-understood setting of cardinality…
This paper considers the classic Online Steiner Forest problem where one is given a (weighted) graph $G$ and an arbitrary set of $k$ terminal pairs $\{\{s_1,t_1\},\ldots ,\{s_k,t_k\}\}$ that are required to be connected. The goal is to…
Backtracking has been widely used for solving problems in artificial intelligence (AI), including constraint satisfaction problems and combinatorial optimization problems. Good branching heuristics can efficiently improve the performance of…
Graph representation of structured data can facilitate the extraction of stereoscopic features, and it has demonstrated excellent ability when working with deep learning systems, the so-called Graph Neural Networks (GNNs). Choosing a…
Under circumstances of heterophily, where nodes with different labels tend to be connected based on semantic meanings, Graph Neural Networks (GNNs) often exhibit suboptimal performance. Current studies on graph heterophily mainly focus on…
Graph neural networks (GNNs) manifest pathologies including over-smoothing and limited discriminating power as a result of suboptimally expressive aggregating mechanisms. We herein present a unifying framework for stochastic aggregation…
We present a learning-based approach to computing solutions for certain NP-hard problems. Our approach combines deep learning techniques with useful algorithmic elements from classic heuristics. The central component is a graph…
Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…
The ability to compute similarity scores between graphs based on metrics such as Graph Edit Distance (GED) is important in many real-world applications. Computing exact GED values is typically an NP-hard problem and traditional algorithms…
In this paper, from a theoretical perspective, we study how powerful graph neural networks (GNNs) can be for learning approximation algorithms for combinatorial problems. To this end, we first establish a new class of GNNs that can solve a…
Generative adversarial network (GAN) has gotten wide re-search interest in the field of deep learning. Variations of GAN have achieved competitive results on specific tasks. However, the stability of training and diversity of generated…
Graph sparsification is to approximate an arbitrary graph by a sparse graph and is useful in many applications, such as simplification of social networks, least squares problems, numerical solution of symmetric positive definite linear…
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…
In mathematical optimization, second-order Newton's methods generally converge faster than first-order methods, but they require the inverse of the Hessian, hence are computationally expensive. However, we discover that on sparse graphs,…
Managing radio spectrum resources is a crucial issue. The frequency assignment problem (FAP) basically aims to allocate, in an efficient manner, limited number of frequencies to communication links. Geographically close links, however,…
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…