Optimal parallel 3-colouring algorithm for rooted trees and its application
A new optimal parallel algorithm for 3-colouring rooted trees with maximum degree Δ is presented. The algorithm runs in O(Δ log n/log log n) time on a CRCW PRAM using O(Δ n log log n/log n) processors. This technique is used to develop optimal algorithms for several graph problems including (Δ+1)-colouring of constant degree graphs, 7-colouring of planar graphs or finding a maximal independent set in a planar graph. The technique can be applied to expression tree evaluation as well and yields an optimal logarithmic time algorithm.
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