research-article

ColPack: Software for graph coloring and related problems in scientific computing

Authors:

Assefaw H. Gebremedhin,

Md. Mostofa Ali Patwary,

Alex PothenAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 40, Issue 1

Article No.: 1, Pages 1 - 31

https://doi.org/10.1145/2513109.2513110

Published: 03 October 2013 Publication History

Abstract

We present a suite of fast and effective algorithms, encapsulated in a software package called ColPack, for a variety of graph coloring and related problems. Many of the coloring problems model partitioning needs arising in compression-based computation of Jacobian and Hessian matrices using Algorithmic Differentiation. Several of the coloring problems also find important applications in many areas outside derivative computation, including frequency assignment in wireless networks, scheduling, facility location, and concurrency discovery and data movement operations in parallel and distributed computing. The presentation in this article includes a high-level description of the various coloring algorithms within a common design framework, a detailed treatment of the theory and efficient implementation of known as well as new vertex ordering techniques upon which the coloring algorithms rely, a discussion of the package's software design, and an illustration of its usage. The article also includes an extensive experimental study of the major algorithms in the package using real-world as well as synthetically generated graphs.

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Index Terms

ColPack: Software for graph coloring and related problems in scientific computing
1. Mathematics of computing
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization
  2. Randomness, geometry and discrete structures

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cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 40, Issue 1

September 2013

165 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/2513109

Issue’s Table of Contents

Copyright © 2013 ACM.

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Publication History

Published: 03 October 2013

Accepted: 01 February 2013

Revised: 01 March 2012

Received: 01 October 2010

Published in TOMS Volume 40, Issue 1

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https://doi.org/10.3390/ijtpp9020020
Yuan FYang XLi SDong DHuang CWang Z(2024)Optimizing Multi-Grid Preconditioned Conjugate Gradient Method on Multi-CoresIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2024.337247335:5(768-779)Online publication date: 1-May-2024
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