Sublinear Algorithms for Spectral Graph Clustering

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In the classical NP-hard (metric) 𝑘-median problem, we are given a set of 𝑛 clients and centers with metric distances between them, along with an integer parameter 𝑘 ≥ 1. The objective is to select a subset of 𝑘 open centers that minimizes the total distan ...

Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem. Spectral algorithms ...

Clustering in education, particularly in large-scale online environments like MOOCs, is essential for understanding and adapting to diverse student needs. However, the effectiveness of clustering depends on its interpretability, which becomes challenging w ...

This paper offers a new algorithm to efficiently optimize scheduling decisions for dial-a-ride problems (DARPs), including problem variants considering electric and autonomous vehicles (e-ADARPs). The scheduling heuristic, based on linear programming theor ...

In light of the challenges posed by climate change and the goals of the Paris Agreement, electricity generation is shifting to a more renewable and decentralized pattern, while the operation of systems like buildings is increasingly electrified. This calls ...

Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...

Urban proximity planning is foreseen as a solution to foster a “sustainable” city, including economic viability, environmental soundness and social inclusivity. This paper focuses on the inclusivity aspects by questioning the adoption of urban proximities: ...

We introduce an algorithm to reconstruct a mesh from discrete samples of a shape's Signed Distance Function (SDF). A simple geometric reinterpretation of the SDF lets us formulate the problem through a point cloud, from which a surface can be extracted wit ...

In this thesis we will present and analyze randomized algorithms for numerical linear algebra problems. An important theme in this thesis is randomized low-rank approximation. In particular, we will study randomized low-rank approximation of matrix functio ...

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

The metric backbone of a weighted graph is the union of all-pairs shortest paths. It is obtained by removing all edges

(u,v)

that are not the shortest path between

u

and

v

. In networks with well-separated communities, the metric backbone tends to pre ...

We examine the connection of two graph parameters, the size of a minimum feedback arcs set and the acyclic disconnection. A feedback arc set of a directed graph is a subset of arcs such that after deletion the graph becomes acyclic. The acyclic disconnecti ...

Operators from various industries have been pushing the adoption of wireless sensing nodes for industrial monitoring, and such efforts have produced sizeable condition monitoring datasets that can be used to build diagnosis algorithms capable of warning ma ...

We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...

Technology mapping transforms a technology-independent representation into a technology-dependent one given a library of cells. This process is performed by means of local replacements that are extracted by matching sections of the subject graph to library ...

We propose an adaptive quantum algorithm to prepare accurate variational time evolved wave functions. The method is based on the projected variational quantum dynamics (pVQD) algorithm, that performs a global optimization with linear scaling in the number ...

Graph neural networks (GNNs) have demonstrated promising performance across various chemistry-related tasks. However, conventional graphs only model the pairwise connectivity in molecules, failing to adequately represent higher order connections, such as m ...

In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...

Distributed learning is the key for enabling training of modern large-scale machine learning models, through parallelising the learning process. Collaborative learning is essential for learning from privacy-sensitive data that is distributed across various ...

Materials for high -temperature environments are actively being investigated for deployment in aerospace and nuclear applications. This study uses computational approaches to unravel the crystallography and thermodynamics of a promising class of refractory ...

Sublinear Algorithms for Spectral Graph Clustering

Chattez avec Graph Search

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