Abstract
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 two from each other. Application examples include numerical optimization and channel assignment. We present the first distributed-memory heuristic algorithm for this NP-hard problem. Parallel speedup is achieved through graph partitioning, speculative (iterative) coloring, and a BSP-like organization of computation. Experimental results show that the algorithm is scalable, and compares favorably with an alternative approach—solving the problem on a graph G by first constructing the square graph G 2 and then applying a parallel distance-1 coloring algorithm on G 2.
This work was supported in part by NSF grants ACI-0203722, ACI-0203846, ANI-0330612, CCF-0342615, CNS-0426241, NIH NIBIB BISTI P20EB000591, Ohio Board of Regents BRTTC BRTT02-0003, Ohio Supercomputing Center PAS0052, and SNL Doc.No: 283793. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin company, for the U.S. DOE’s National Nuclear Security Administration under contract DE-AC04-94AL85000.
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References
Gebremedhin, A.H., Manne, F., Pothen, A.: What color is your jacobian? Graph coloring for computing derivatives. SIAM Rev (2005) (to appear)
Krumke, S.O., Marathe, M.V., Ravi, S.S.: Models and approximation algorithms for channel assignment in radio networks. Wireless Networks 7, 575–584 (2001)
Vazirani, V.V.: Approximation Algorithms. Springer, Heidelberg (2001)
Ferreira, A., Pérennes, S., Richa, A.W., Rivano, H., Stier, N.: Models, complexity and algorithms for the design of multi-fiber wdm networks. Telecommunication Systems 24, 123–138 (2003)
McCormick, S.T.: Optimal approximation of sparse hessians and its equivalence to a graph coloring problem. Math. Programming 26, 153–171 (1983)
Boman, E.G., Bozdağ, D., Catalyurek, U., Gebremedhin, A.H., Manne, F.: A scalable parallel graph coloring algorithm for distributed memory computers. In: EuroPar (2005) (to appear)
Gebremedhin, A.H., Manne, F.: Scalable parallel graph coloring algorithms. Concurrency: Practice and Experience 12, 1131–1146 (2000)
Gebremedhin, A.H., Manne, F., Woods, T.: Speeding up parallel graph coloring. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds.) PARA 2004. LNCS, vol. 3732, pp. 1079–1088. Springer, Heidelberg (2006)
Jones, M.T., Plassmann, P.: A parallel graph coloring heuristic. SIAM-SC 14, 654–669 (1993)
Gebremedhin, A.H., Manne, F., Pothen, A.: Parallel distance-k coloring algorithms for numerical optimization. In: Monien, B., Feldmann, R.L. (eds.) Euro-Par 2002. LNCS, vol. 2400, pp. 912–921. Springer, Heidelberg (2002)
Test data from the parasol project, http://www.parallab.uib.no/projects/parasol/data/
University of florida matrix collection, http://www.cise.ufl.edu/research/sparse/matrices/
Strout, M.M., Hovland, P.D.: Metrics and models for reordering transformations. In: Proceedings of MSP 2004, pp. 23–34 (2004)
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Bozdağ, D., Catalyurek, U., Gebremedhin, A.H., Manne, F., Boman, E.G., Özgüner, F. (2005). A Parallel Distance-2 Graph Coloring Algorithm for Distributed Memory Computers. In: Yang, L.T., Rana, O.F., Di Martino, B., Dongarra, J. (eds) High Performance Computing and Communications. HPCC 2005. Lecture Notes in Computer Science, vol 3726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11557654_90
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