Approximate counting, uniform generation and rapidly mixing Markov chains
Information and Computation
On the second eigenvalue of random regular graphs
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Existence and Construction of Edge-Disjoint Pathson Expander Graphs
SIAM Journal on Computing
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Optimal Construction of Edge-Disjoint Paths in Random Graphs
SIAM Journal on Computing
An efficient algorithm for the vertex-disjoint paths problem in random graphs
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
New algorithmic aspects of the Local Lemma with applications to routing and partitioning
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Multicommodity Flow and Circuit Switching
HICSS '98 Proceedings of the Thirty-First Annual Hawaii International Conference on System Sciences-Volume 7 - Volume 7
Universal schemes for parallel communication
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Graph Theory With Applications
Graph Theory With Applications
Approximation algorithms for edge-disjoint paths and unsplittable flow
Efficient Approximation and Online Algorithms
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Given a graph G = (V, E) and a set of κ 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 κ paths so found is edge-disjoint. (For arbitrary graphs the problem is 𝒩𝒫-complete, although it is in 𝒫 if κ is fixed.)We present a polynomial time randomized algorithm for finding edge-disjoint paths in the random regular graph Gn,r, for sufficiently large r. (The graph is chosen first, then an adversary chooses the pairs of end-points.) We show that almost every Gn,r is such that all sets of κ = Ω(n/log n) pairs of vertices can be joined. This is within a constant factor of the optimum.