Efficient Parallel Graph Coloring with Prioritization

Graph coloring is an interesting problem that is intuitive and simple to formulate, yet difficult to solve efficiently. The applications of graph coloring are numerous, ranging from scheduling to solving linear systems. Because graph coloring is computationally intensive, a parallel algorithm is desirable. In this paper, we present a set of parallel graph coloring heuristics and describe their implementation in an environment supporting machine-independent parallel programming. The heuristics are intended to provide consistent, monotonically increasing speedups as the number of processors is increased. We present some performance results that demonstrate the effectiveness of our heuristics and the utility of our approach.

[1]  Vikram A. Saletore,et al.  Machine independent parallel execution of speculative computations , 1992 .

[2]  Mark T. Jones,et al.  Scalable Iterative Solution of Sparse Linear Systems , 1994, Parallel Comput..

[3]  Min-You Wu,et al.  A Dynamic Partitioning Strategy on Distributed Memory Systems , 1990, ICPP.

[4]  Laxmikant V. Kalé,et al.  Consistent Linear Speedups to a First Solution in Parallel State-Space Search , 1990, AAAI.

[5]  D. Werra,et al.  Some experiments with simulated annealing for coloring graphs , 1987 .

[6]  Laxmikant V. Kalé,et al.  A load balancing strategy for prioritized execution of tasks , 1993, [1993] Proceedings Seventh International Parallel Processing Symposium.

[7]  J. J. Moré,et al.  Estimation of sparse jacobian matrices and graph coloring problems , 1983 .

[8]  Keith D. Cooper,et al.  Improvements to graph coloring register allocation , 1994, TOPL.

[9]  B. Ramkumar,et al.  A dynamic and adaptive quiescence detection algorithmAmitabh , 1993 .

[10]  Laxmikant V. Kalé,et al.  The Chare Kernel Parallel Programming Language and System , 1990, ICPP.

[11]  Laxmikant V. Kale,et al.  Parallel problem solving , 1990 .

[12]  Robert H. Halstead,et al.  Parallel Symbolic Computing , 1986, Computer.

[13]  James M. Ortega.  Orderings for Conjugate Gradient Preconditionings , 1991, SIAM J. Optim..

[14]  Wolfgang Fichtner,et al.  A Set of New Mapping and Coloring Heuristics for Distributed-Memory Parallel Processors , 1992, SIAM J. Sci. Comput..

[15]  O. Ore.  The Four-Color Problem , 1967 .

[16]  Laxmikant V. Kalé,et al.  Prioritization in Parallel Symbolic Computing , 1992, Parallel Symbolic Computing.

[17]  Rami G. Melhem,et al.  Multicolor reordering of sparse matrices resulting from irregular grids , 1988, TOMS.

[18]  Daniel Brélaz,et al.  New methods to color the vertices of a graph , 1979, CACM.

[19]  Benjamin W. Wah,et al.  Coping with Anomalies in Parallel Branch-and-Bound Algorithms , 1986, IEEE Transactions on Computers.

[20]  Mark T. Jones,et al.  A Parallel Graph Coloring Heuristic , 1993, SIAM J. Sci. Comput..