Efficient parallel algorithms for computing all pair shortest paths in directed graphs

We present parallel algorithms for computing all pair shortest paths in directed graphs. Our algorithm has time complexityO(f(n)/p+I(n)logn) on the PRAM usingp processors, whereI(n) is logn on the EREW PRAM, log logn on the CCRW PRAM,f(n) iso(n3). On the randomized CRCW PRAM we are able to achieve time complexityO(n3/p+logn) usingp processors.

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