A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
Almost all k-colorable graphs are easy to color
Journal of Algorithms
A parallel graph coloring heuristic
SIAM Journal on Scientific Computing
Scalable iterative solution of sparse linear systems
Parallel Computing
ILUM: a multi-elimination ILU preconditioner for general sparse matrices
SIAM Journal on Scientific Computing
An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications
New methods to color the vertices of a graph
Communications of the ACM
A Scalable Parallel Algorithm for Incomplete Factor Preconditioning
SIAM Journal on Scientific Computing
Estimation of Sparse Hessian Matrices and Graph Coloring Problems
Estimation of Sparse Hessian Matrices and Graph Coloring Problems
Proceedings of the 2nd conference on Computing frontiers
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Graph mining: Laws, generators, and algorithms
ACM Computing Surveys (CSUR)
Evaluating the potential of multithreaded platforms for irregular scientific computations
Proceedings of the 4th international conference on Computing frontiers
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
Memory Performance and Cache Coherency Effects on an Intel Nehalem Multiprocessor System
PACT '09 Proceedings of the 2009 18th International Conference on Parallel Architectures and Compilation Techniques
Why Almost All k-Colorable Graphs Are Easy to Color
Theory of Computing Systems - Special Issue: Theoretical Aspects of Computer Science; Guest Editors: Wolgang Thomas and Pascal Weil
SIAM Journal on Scientific Computing
Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
ColPack: Software for graph coloring and related problems in scientific computing
ACM Transactions on Mathematical Software (TOMS)
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We explore the interplay between architectures and algorithm design in the context of shared-memory platforms and a specific graph problem of central importance in scientific and high-performance computing, distance-1 graph coloring. We introduce two different kinds of multithreaded heuristic algorithms for the stated, NP-hard, problem. The first algorithm relies on speculation and iteration, and is suitable for any shared-memory system. The second algorithm uses dataflow principles, and is targeted at the non-conventional, massively multithreaded Cray XMT system. We study the performance of the algorithms on the Cray XMT and two multi-core systems, Sun Niagara 2 and Intel Nehalem. Together, the three systems represent a spectrum of multithreading capabilities and memory structure. As testbed, we use synthetically generated large-scale graphs carefully chosen to cover a wide range of input types. The results show that the algorithms have scalable runtime performance and use nearly the same number of colors as the underlying serial algorithm, which in turn is effective in practice. The study provides insight into the design of high performance algorithms for irregular problems on many-core architectures.