Abstract
Two parallel algorithms for edge-colouring simple graphs are presented. One takes O(mlogn) time using a polynomial number of processors on an SIMD parallel computer which allows read conflicts but no write conflicts. The second algorithm uses the first in a divide-and-conquer setting and takes O(nlog2 n) time at the cost of a factor of n extra processors on the same model of computation. How to obtain improved time bounds from these algorithms for some special types of graph is also discussed.
Either algorithm uses no more than φe+1 colours where φe is the edge-chromatic number of the graph being coloured. Moreover the expected performance of each of the algorithms is optimal.
This work was done while a research student at Warwick University, Coventry, UK.
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References
M. Atallah and U. Vishkin, "Finding Euler Tours in Parallel", J. Comput. and Syst. Sciences 29, 330–337 (1984).
R.D. Dutton and R.C. Brigham, "A new graph colouring algorithm", Computer J. 24, 85–86 (1981).
A.M. Frieze, "Parallel Algorithms for Finding Hamiltonian Cycles in Random Graphs", Manuscript, Department of Computer Science, Queen Mary College (March 1986).
M.R. Garey and D.S. Johnson, "Computer and Intractability: A Guide to the Theory of NP-completeness", Freeman (1979).
H.N. Grabow and O. Kariv, "Algorithms for Edge Colouring Bipartite Graphs and Multigraphs", SIAM J. Comput. 11, 117–129 (1982).
A.M. Gibbons, "Algorithmic Graph Theory", Cambridge University Press (1985).
A.M. Gibbons and O.A. Ogunyode, "A Polynomial-Time Algorithm to Edge-Colour Almost All Graphs Using φe Colours", Theory of Computation, Report No. 68, (September 1984).
I. Holyer, "The NP-completeness of Edge-Colouring", SIAM J. Comput. 10, 718–720 (1981).
F.T. Leighton, "A graph coloring algorithm for large scheduling problems", J. Res. Natn. Bur. Stand. 84, 489–506 (1979).
G. Lev, N. Pippenger and L.G. Valliant, "A Fast Parallel Algorithm for Routing in Permutation Networks", IEEE Trans. Comput., C-30, 93–110 (1981).
O.A. Ogunyode, "Approximation and Parallel Algorithms for Some NP-Hard Problems", Ph.D. Thesis, Department of Computer Science, University of Warwick (August 1986).
M.J. Quinn and N. Deo, "A Parallel Approximate Algorithm for the Euclidean Traveling Salesman Problem", Report CS-83-105, Computer Science Department, Washington State University, Pullman (1983).
Y.H. Tsin and F.Y. Chin, "Efficient Parallel Algorithms for a Class of Graph Theoretic Problems", SIAM J. Comput. 13, 580–599 (1984).
V.G. Vizing, "On an estimate of the chromatic class of p-graph", Diskret. Analiz. 3, 25–30 (1964).
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© 1987 Springer-Verlag Berlin Heidelberg
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Ogunyode, O.A. (1987). Parallel algorithms for approximate edge colouring of simple graphs. In: Nori, K.V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1987. Lecture Notes in Computer Science, vol 287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18625-5_52
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DOI: https://doi.org/10.1007/3-540-18625-5_52
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