An Optimal Parallel Processor Bound in Strong Orientation of an Undirected Graph

Recently, Atal lah [1] presented an algori thm for assigning directions to the edges of a connected, bridgeless undirected graph so that the resulting directed graph is strong in the sense that there is a directed path f rom u to v for every two vertices u, v in it. Atallah indicated that a direct implementat ion of that algori thm takes O(log 2 n) time with O(n 4) processors on the P R A M a S I M D shared m e m o r y model allowing read but not write conf l i c t s -where n is the size of the vertex set. He then proceeded to give an implementa t ion which takes O(log 2 n) t ime with O(n 3) processors. Our aim is to present an implementa t ion which takes O(log 2 n) t ime with n [ n / l o g 2 n] processors on the PRAM. This result reduces the number of processors used by a factor of n log 2 n and is optimal for dense graphs. In Table 1 we list some opt imal results which are to be used in the following discussion.