Abstract
A modification of Dantzig's algorithm for the all pairs shortest paths problem is given. The new algorithm applies only to graphs with nonnegative arc lengths. For an N-node complete graph it has a worst case running time of 2 3 N 3 triple operations of the form D ij : = min( D ij , D ik + D kj ) and N 2 log N other comparisons. This contrasts with a lower bound of N( N − 1) ( N − 2) triples in any pure triple operation algorithm, and seems to be the first algorithm in which no operation need be repeated N 3 times. Sparsity and some other conditions may also be utilized.
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