Software for estimating sparse Jacobian matrices
ACM Transactions on Mathematical Software (TOMS)
Software for estimating sparse Hessian matrices
ACM Transactions on Mathematical Software (TOMS)
The cyclic coloring problem and estimation of spare hessian matrices
SIAM Journal on Algebraic and Discrete Methods
Almost all k-colorable graphs are easy to color
Journal of Algorithms
Scalable iterative solution of sparse linear systems
Parallel Computing
Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++
ACM Transactions on Mathematical Software (TOMS)
ILUM: a multi-elimination ILU preconditioner for general sparse matrices
SIAM Journal on Scientific Computing
The Efficient Computation of Sparse Jacobian Matrices Using Automatic Differentiation
SIAM Journal on Scientific Computing
New methods to color the vertices of a graph
Communications of the ACM
On algorithms for efficient data migration
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
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ACM Computing Surveys (CSUR)
New Acyclic and Star Coloring Algorithms with Application to Computing Hessians
SIAM Journal on Scientific Computing
A framework for scalable greedy coloring on distributed-memory parallel computers
Journal of Parallel and Distributed Computing
Improving the Performance of Graph Coloring Algorithms through Backtracking
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Efficient Computation of Sparse Hessians Using Coloring and Automatic Differentiation
INFORMS Journal on Computing
SIAM Journal on Scientific Computing
New multithreaded ordering and coloring algorithms for multicore architectures
Euro-Par'11 Proceedings of the 17th international conference on Parallel processing - Volume Part II
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
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Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis
The Art of Differentiating Computer Programs: An Introduction to Algorithmic Differentiation
The Art of Differentiating Computer Programs: An Introduction to Algorithmic Differentiation
Register allocation via coloring
Computer Languages
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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.