相关论文: Extremal Optimization for Graph Partitioning

Finding a maximum-cardinality or maximum-weight matching in (edge-weighted) undirected graphs is among the most prominent problems of algorithmic graph theory. For $n$-vertex and $m$-edge graphs, the best known algorithms run in…

This note explores the applicability of unsupervised machine learning techniques towards hard optimization problems on random inputs. In particular we consider Graph Neural Networks (GNNs) -- a class of neural networks designed to learn…

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

We investigate the phase transition of the 3-coloring problem on random graphs, using the extremal optimization heuristic. 3-coloring is among the hardest combinatorial optimization problems and is closely related to a 3-state…

We propose a protocol optimization technique that is applicable to both weighted or unweighted graphs. Our aim is to explore by how much a small variation around the Shortest Path or Optimal Path protocols can enhance protocol performance.…

Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…

The best practical techniques for exact solution of instances of the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a branch-and-bound framework, working with a…

Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem…

Partitioning an input graph over a set of workers is a complex operation. Objectives are twofold: split the work evenly, so that every worker gets an equal share, and minimize edge cut to achieve a good work locality (i.e. workers can work…

Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks.…

Graph partitioning aims to divide a graph into disjoint subsets while optimizing a specific partitioning objective. The majority of formulations related to graph partitioning exhibit NP-hardness due to their combinatorial nature.…

This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…

The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…

The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…

Edge-centric distributed computations have appeared as a recent technique to improve the shortcomings of think-like-a-vertex algorithms on large scale-free networks. In order to increase parallelism on this model, edge partitioning -…

The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…

Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…

In this paper, we develop semi-external and external memory algorithms for graph partitioning and clustering problems. Graph partitioning and clustering are key tools for processing and analyzing large complex networks. We address both…

A thesis submitted for the degree of Doctor of Philosophy of The Australian National University. In this work we introduce several new optimisation methods for problems in machine learning. Our algorithms broadly fall into two categories:…

Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class…