Efficient parallel and sequential algorithms for 4-coloring perfect planar graphs
We present an efficient algorithm for 4-coloring perfect planar graphs. The best previously known algorithm for this problem takesO(n 3/2) sequential time, orO(log4 n) parallel time withO(n3) processors. The sequential implementation of our algorithm takesO(n logn) time. The parallel implementation of our algorithm takesO(log3 n) time withO(n) processors on a PRAM.
Key wordsPlanar graphs Perfect graphs 4-Coloring algorithm
Unable to display preview. Download preview PDF.
- J. A. Bondy and U. S. R. Murty,Graph Theory with Applications, North-Holland, New York, 1980.Google Scholar
- R. Cole, Parallel Merge Sort,Proc. 27th IEEE Symposium on Foundations of Computer Science, 1986, pp. 511–517.Google Scholar
- A. V. Goldberg, S. A. Plotkin, and G. E. Shannon, Parallel Symmetry Breaking in Sparse Graphs,Proc. 19th ACM Symposium on Theory of Computing, 1987, pp. 315–325.Google Scholar
- T. Hagerup, M. Chrobak, and K. Diks, Parallel 5-Coloring of Planar Graphs,Proc. 14th International Colloquium on Automata, Language and Programming, 1987, pp. 304–313.Google Scholar
- P. N. Klein and J. H. Reif, An Efficient Parallel Algorithm for Planarity,Proc. 27th IEEE Symposium on Foundations of Computer Science, 1986, pp. 465–477.Google Scholar
- D. Matula, Y. Shiloach, and R. Tarjan, Two Linear Time Algorithms for 5-Coloring a Planar Graph, Technical Report STAN-CS-80-830, Department of Computer Science, Stanford University, 1980.Google Scholar
- G. Miller and J. Reif, Parallel Tree Contraction and Its Applications,Proc. 26th IEEE Symposium on Foundations of Computer Science, 1985, pp. 478–489.Google Scholar
- I. A. Stewart, An Algorithm for Coloring Perfect Planar Graphs,Proc. 7th Conference on Foundations of Software Technology and Theoretical Computer Science, Lecture Notes in Computer Science, Vol. 287, Springer-Verlag, Berlin, 1987, pp. 58–63.Google Scholar
- I. A. Stewart, A Parallel Algorithm to Four-Color a Perfect Planar Graph, presented at the 14th International Workshop on Graph-Theoretic Concepts in Computer Science, Amsterdam, June 1988.Google Scholar