Abstract
A node ranking of a graph G = (V, E) is a proper node coloring C: V →ℕ such that any path in G with end nodes x, y fulfilling C(x) = C(y) contains an internal node z with C(z) > C(x). In the on-line version of the node ranking problem, the nodes v 1, v 2,..., v n are coming one by one in an arbitrary order; and only the edges of the induced subgraph G[{v 1, v 2,..., v i }] are known when the color for the node v i be chosen. And the assigned color can not be changed later. In this paper, we present a parallel algorithm to find an on-line node ranking for general tree. Our parallel algorithm needs O(nlog2 n ) time with using O(n 3 / log2 n) processors on CREW PRAM model.
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Lee, CW., Juan, J.ST., Wu, TL. (2009). An On-Line Parallel Algorithm for Node Ranking of Trees. In: Hua, A., Chang, SL. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2009. Lecture Notes in Computer Science, vol 5574. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03095-6_37
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DOI: https://doi.org/10.1007/978-3-642-03095-6_37
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