Scalable iterative solution of sparse linear systems
Parallel Computing
ILUM: a multi-elimination ILU preconditioner for general sparse matrices
SIAM Journal on Scientific Computing
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Hypergraph-Partitioning-Based Decomposition for Parallel Sparse-Matrix Vector Multiplication
IEEE Transactions on Parallel and Distributed Systems
A Scalable Parallel Algorithm for Incomplete Factor Preconditioning
SIAM Journal on Scientific Computing
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
Zoltan Data Management Service for Parallel Dynamic Applications
Computing in Science and Engineering
Parallel Distance-k Coloring Algorithms for Numerical Optimization
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
Coloring Powers of Planar Graphs
SIAM Journal on Discrete Mathematics
End-to-end packet-scheduling in wireless ad-hoc networks
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Parallel Scientific Computation: A Structured Approach Using BSP and MPI
Parallel Scientific Computation: A Structured Approach Using BSP and MPI
Metrics and models for reordering transformations
MSP '04 Proceedings of the 2004 workshop on Memory system performance
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
Efficient Computation of Sparse Hessians Using Coloring and Automatic Differentiation
INFORMS Journal on Computing
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
A parallel distance-2 graph coloring algorithm for distributed memory computers
HPCC'05 Proceedings of the First international conference on High Performance Computing and Communications
New multithreaded ordering and coloring algorithms for multicore architectures
Euro-Par'11 Proceedings of the 17th international conference on Parallel processing - Volume Part II
ColPack: Software for graph coloring and related problems in scientific computing
ACM Transactions on Mathematical Software (TOMS)
Scientific Programming - A New Overview of the Trilinos Project --Part 1
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The distance-2 graph coloring problem aims at partitioning the vertex set of a graph into the fewest sets consisting of vertices pairwise at distance greater than 2 from each other. Its applications include derivative computation in numerical optimization and channel assignment in radio networks. We present efficient, distributed-memory, parallel heuristic algorithms for this NP-hard problem as well as for two related problems used in the computation of Jacobians and Hessians. Parallel speedup is achieved through graph partitioning, speculative (iterative) coloring, and a bulk synchronous parallel-like organization of parallel computation. Results from experiments conducted on a PC cluster employing up to 96 processors and using large-size real-world as well as synthetically generated test graphs show that the algorithms are scalable. In terms of quality of solution, the algorithms perform remarkably well—the numbers of colors used by the parallel algorithms are observed to be very close to the numbers used by their sequential counterparts, which in turn are quite often near optimal. Moreover, the experimental results show that the parallel distance-2 coloring algorithm compares favorably with the alternative approach of solving the distance-2 coloring problem on a graph $\mathcal{G}$ by first constructing the square graph $\mathcal{G}^2$ and then applying a parallel distance-1 coloring algorithm on $\mathcal{G}^2$. Implementations of the algorithms are made available via the Zoltan toolkit.