Related papers: Aggregative Coarsening for Multilevel Hypergraph P…
We describe an approach to parallel graph partitioning that scales to hundreds of processors and produces a high solution quality. For example, for many instances from Walshaw's benchmark collection we improve the best known partitioning.…
A graph based matching is used to construct aggregation for algebraic multigrid. Effects of inexact coarse grid solve is analyzed numerically for a highly discontinuous convection diffusion coefficient matrix and problems from Florida…
Balanced hypergraph partitioning is an NP-hard problem with many applications, e.g., optimizing communication in distributed data placement problems. The goal is to place all nodes across $k$ different blocks of bounded size, such that…
Hypergraphs, increasingly utilised for modelling complex and diverse relationships in modern networks, gain much attention representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery is one of the…
This paper describes a massively parallel algebraic multigrid method based on non-smoothed aggregation. It is especially suited for solving heterogeneous elliptic problems as it uses a greedy heuristic algorithm for the aggregation that…
Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that…
In recent years, significant advances have been made in the design and evaluation of balanced (hyper)graph partitioning algorithms. We survey trends of the last decade in practical algorithms for balanced (hyper)graph partitioning together…
We describe a new optimization scheme for finding high-quality correlation clusterings in planar graphs that uses weighted perfect matching as a subroutine. Our method provides lower-bounds on the energy of the optimal correlation…
We present a multi-level graph partitioning algorithm based on the extreme idea to contract only a single edge on each level of the hierarchy. This obviates the need for a matching algorithm and promises very good partitioning quality since…
Modularity is one of the most widely used quality measures for graph clusterings. Maximizing modularity is NP-hard, and the runtime of exact algorithms is prohibitive for large graphs. A simple and effective class of heuristics coarsens the…
We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to…
This paper presents algorithms for hierarchical, agglomerative clustering which perform most efficiently in the general-purpose setup that is given in modern standard software. Requirements are: (1) the input data is given by pairwise…
Partitioning large matrices is an important problem in distributed linear algebra computing (used in ML among others). Briefly, our goal is to perform a sequence of matrix algebra operations in a distributed manner (whenever possible) on…
Linear solvers for large and sparse systems are a key element of scientific applications, and their efficient implementation is necessary to harness the computational power of current computers. Algebraic MultiGrid (AMG) preconditioners are…
Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…
The general method of graph coarsening or graph reduction has been a remarkably useful and ubiquitous tool in scientific computing and it is now just starting to have a similar impact in machine learning. The goal of this paper is to take a…
Visual recognition requires rich representations that span levels from low to high, scales from small to large, and resolutions from fine to coarse. Even with the depth of features in a convolutional network, a layer in isolation is not…
Hierarchical abstractions are a methodology for solving large-scale graph problems in various disciplines. Coarsening is one such approach: it generates a pyramid of graphs whereby the one in the next level is a structural summary of the…
We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of an LP relaxation of ultrametric rounding. To solve this LP efficiently we introduce a dual cutting plane scheme that uses minimum cost perfect…
We present a multi-level graph partitioning algorithm using novel local improvement algorithms and global search strategies transferred from the multi-grid community. Local improvement algorithms are based max-flow min-cut computations and…