Abstract
For a positive integer c, a c-vertex-ranking of a graph G = (V, E) is a labeling of the vertices of G with integers such that, for any label i, deletion of all vertices with labels > i leaves connected components, each having at most c vertices with label i. The c-vertex-ranking problem is to find a c-vertex-ranking of a given graph using the minimum number of ranks. In this paper we give an optimal parallel algorithm for solving the c-vertex-ranking problem on trees that takes O(log2 n) parallel time using linear number of operations on the EREW PRAM model.
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References
Abrahamson, K., Dadoun, N., Kirkpatrick, D.G., Przytycka, T.: A simple parallel tree contraction algorithm. Journal of Algorithms 10, 287–302 (1989)
Bodlaender, H., Deogun, J.S., Jansen, K., Kloks, T., Müller, H.H., Tuza, Z.: Rankings of graphs. SIAM Journal of Discrete Math. 21, 168–181 (1998)
de la Torre, P., Greenlaw, R., Przytycka, T.M.: Optimal tree ranking is in NC. Parallel Processing Letters 2, 31–41 (1992)
Iyer, A.V., Ratliff, H.D., Vijayan, G.: Optimal vertex ranking of trees. Information Processing Letters 28, 225–229 (1988)
Já, J.J.: An Introduction to Parallel Algorithms. Addison-Wesley, Reading (1992)
Kashem, M.A., Zhou, X., Nishizeki, T.: Algorithms for generalized vertexrankings of partial k-trees. Theoretical Computer Science 240, 407–427 (2000)
Pothen, A.: The complexity of optimal elimination trees, Technical Report CS-88-13, Pennsylvania State University, U.S.A (1988)
Schäffer, A.A.: Optimal vertex ranking of trees in linear time. Information Processing Letters 33, 91–99 (1989)
Zhou, X., Nagai, N., Nishizeki, T.: Generalized vertex-rankings of trees. Information Processing Letters 56, 321–328 (1995)
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© 2003 Springer-Verlag Berlin Heidelberg
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Kashem, M.A., Rahman, M.Z. (2003). An Optimal Parallel Algorithm for c-Vertex-Ranking of Trees. In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_48
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DOI: https://doi.org/10.1007/978-3-540-24587-2_48
Publisher Name: Springer, Berlin, Heidelberg
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