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# Optimal Construction of Edge-Disjoint Paths in Random Graphs

Symposium on Discrete Algorithms, no. 2 (1999): 541-573

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Given a graph G=(V,E) with n vertices, m edges, and a family of $\kappa$ pairs of vertices in $V$, we are interested in finding for each pair (ai, bi) a path connecting ai to bi such that the set of $\kappa$ paths so found is edge disjoint. (For arbitrary graphs the problem is ${\cal NP}$-complete, although it is in ${\cal P}$ if $\kappa$...More

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