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(n 3). On the randomized CRCW PRAM we are able to achieve time complexityO(n 3/p+logn) usingp processors.

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