Weconsider parallel shortest-paths computations in weighted undirected graphsG=(V, E),
wheren=| V| andm=| E|. The standardO (n3) work path-doubling (Floyd-Warshall) algorithm
consists ofO (logn) phases, where in each phase, for every triplet of vertices (u1, u2, u3)∈
V3, the distance betweenu1andu3is updated to be no more than the sum of the previous-
phase distances between {u1, u2} and {u2, u3}. We introduce a new NC algorithm that for δ=
o (n), considers onlyO (nδ2) triplets. Our algorithm performsÕ (nδ2) work and …

The author considers parallel shortest-path computations in weighted undirected graphs
G=(V, E), where n= mod V mod and m= mod E mod. The standard path-doubling algorithms
consists of O (log n) phases, where in each phase, for every triple of vertices (u/sub 1/, u/sub
2/, u/sub 3/) in V/sup 3/, she updates the distance between u/sub 1/and u/sub 3/to be no
more than the sum of the previous-phase distances between (u/sub 1/, u/sub 2/) and (u/sub
2/, u/sub 3/). The work performed in each phase, O (n/sup 3/)(linear in the number of triples) …