# A Software Package for Partitioning Unstructured Graphs , Partitioning Meshes , and Computing Fill-Reducing Orderings of Sparse Matrices Version 5 . 0

@inproceedings{Karypis1998ASP, title={A Software Package for Partitioning Unstructured Graphs , Partitioning Meshes , and Computing Fill-Reducing Orderings of Sparse Matrices Version 5 . 0}, author={George Karypis}, year={1998} }

∗METIS is copyrighted by the regents of the University of Minnesota . This work was supported by IST/BMDO through Army Research O ffice contract DA/DAAH04-93-G-0080, and by Army High Performanc e Computing Research Center under the auspices of the Depart ment of the Army, Army Research Laboratory cooperative agreement number DAA H04-95-2-0003/contract number DAAH04-95-C-0008, the con tent of which does not necessarily reflect the position or the policy of the gove rnment, and no official…

## 186 Citations

### International Workshop on Parallel Matrix Algorithms and Applications Parallel Restricted Maximum Likelihood Estimation for Linear Models with a Dense Exogenous Matrix. Iterative Methods Least-squares Polynomial Preconditioners for Symmetric Indefinite Linear Parallel Computation of Generalized Eige

- Computer Science
- 2000

This tutorial provides an overview of the recent developments and state of the art in the areas of high performance hardware, tools and environments, and libraries as related to the matrix algorithms and some aspects of iterative and direct methods for the (partial) eigensolution of real symmetric matrices are addressed.

### Research Reports on Mathematical and Computing Sciences Department of Mathematical and Computing Sciences Tokyo Institute of Technology SERIES B : Operations Research

- Computer Science
- 2004

The SDPA-C (SemiDefinite Programming Algorithm – Completion method) is a software package designed for solving large scale sparse SDPs (semidefinite programming problems) using the positive definite matrix completion theory.

### A Highly Scalable Parallel Implementation of Balancing Domain Decomposition by Constraints

- Computer ScienceSIAM J. Sci. Comput.
- 2014

A novel parallelization approach of two-level balancing domain decomposition by constraints preconditioning based on overlapping of fine-grid and coarse-grid duties in time is proposed.

### Shape optimizing load balancing for MPI-parallel adaptive numerical simulations

- Computer ScienceGraph Partitioning and Graph Clustering
- 2012

This work explores the promising diffusion-based multilevel graph partitioning algorithm DibaP, and describes the evolution of the algorithm and reports on its MPI implementation PDibaP for parallelism with distributed memory.

### PMORSy: parallel sparse matrix ordering software for fill-in minimization†

- Computer ScienceOptim. Methods Softw.
- 2017

The NP-complete fill-in minimization problem is solved by means of multilevel nested dissection algorithm with modifications for vertex separators and parallel processing is done in a task-based fashion with the granularity tuning.

### Multilevel Hypergraph Partitioning with Vertex Weights Revisited

- Computer Science, MathematicsSEA
- 2021

This work develops an approach based on an assignment of heavy vertices as fixed vertices to both blocks of the bisection (which it is called a prepacking) and uses theoretical results to prove that the balance of the final partition can be guaranteed.

### Parallel Computing Techniques for Large-Scale Reservoir Simulation of Multi- Component and Multiphase Fluid Flow

- Computer Science
- 2001

The results indicate that the parallel code TOUGH2 is significantly improve c apacity and efficiency for large-scale simulations, and the METIS software package for partitioning unstructured graph and meshes is adopted for domain partitioning.

### An improved recursive graph bipartitioning algorithm for well balanced domain decomposition

- Computer Science2014 21st International Conference on High Performance Computing (HiPC)
- 2014

This paper revisit the original algorithm introduced by Lipton, Rose and Tarjan in 1979 which performed the recursion for nested dissection in a particular manner and proposes several variations of the existing algorithms in the multilevel Scotch partitioner that take into account multiple criteria.

### Optimized Schwarz and 2-Lagrange Multiplier Methods for Multiscale Elliptic PDEs

- Computer ScienceSIAM J. Sci. Comput.
- 2015

This article formulate and analyze a two-level preconditioner for optimized Schwarz and 2-Lagrange multiplier methods for PDEs with highly heterogeneous (multiscale) diffusion coefficients and shows that the GMRES algorithm applied to the heterogeneous system converges in O(1/\epsilon) iterations.

### TOUGH 2 _ MP : A PARALLEL VERSION OF TOUGH 2

- Computer Science
- 2003

The development of the TOUGH2_MP is reviewed, the basic features, modules, and their applications are discussed, and the standard message-passing interface is adopted for communication among processors.

## References

SHOWING 1-10 OF 15 REFERENCES

### A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs

- Computer ScienceSIAM J. Sci. Comput.
- 1998

This work presents a new coarsening heuristic (called heavy-edge heuristic) for which the size of the partition of the coarse graph is within a small factor of theSize of the final partition obtained after multilevel refinement, and presents a much faster variation of the Kernighan--Lin (KL) algorithm for refining during uncoarsening.

### Multilevel Algorithms for Multi-Constraint Graph Partitioning

- Computer ScienceProceedings of the IEEE/ACM SC98 Conference
- 1998

This work focuses on developing new types of heuristics for coarsening, initial partitioning, and refinement that are capable of successfully handling multiple constraints that underlay many existing and emerging large-scale scientific simulations.

### Fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems

- Computer ScienceConcurr. Pract. Exp.
- 1994

A multilevel version of RSB is introduced that attains about an order-of-magnitude improvement in run time on typical examples of unstructured meshes used in several large-scale scientific and engineering problems.

### Multilevel k-way Partitioning Scheme for Irregular Graphs

- Computer ScienceJ. Parallel Distributed Comput.
- 1998

In this paper, we present and study a class of graph partitioning algorithms that reduces the size of the graph by collapsing vertices and edges, we find ak-way partitioning of the smaller graph, and…

### A multilevel algorithm for partitioning graphs

- Computer Science
- 1995

A multilevel algorithm for graph partitioning in which the graph is approximated by a sequence of increasingly smaller graphs, and the smallest graph is then partitioned using a spectral method, and this partition is propagated back through the hierarchy of graphs.

### The Chaco user`s guide. Version 1.0

- Computer Science
- 1993

The Chaco software package allows for recursive application of any of several different methods for finding small edge separators in weighted graphs, including inertial, spectral, Kernighan-Lin and multilevel methods in addition to several simpler strategies.

### Multilevel hypergraph partitioning: application in VLSI domain

- Computer ScienceDAC
- 1997

The experiments show that the multilevel hypergraph partitioning algorithm produces high quality partitioning in relatively small amount of time and outperforms other schemes (in hyperedge cut) quite consistently with larger margins.

### Highly Scalable Parallel Algorithms for Sparse Matrix Factorization

- Computer ScienceIEEE Trans. Parallel Distributed Syst.
- 1997

The first algorithms to factor a wide class of sparse matrices that are asymptotically as scalable as dense matrix factorization algorithms on a variety of parallel architectures are presented.

### An efficient heuristic procedure for partitioning graphs

- Computer ScienceBell Syst. Tech. J.
- 1970

A heuristic method for partitioning arbitrary graphs which is both effective in finding optimal partitions, and fast enough to be practical in solving large problems is presented.

### Introduction to parallel computing: design and analysis of algorithms

- Computer Science
- 1994

Performance and Scalability of Parallel Systems, General Issues in Mapping Systolic Systems Onto Parallel Computers, and Speedup Anomalies in Parallel Search Algorithms.