Methods for message routing in parallel machines
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Fast Algorithms for Routing Around Faults in Multibutterflies and Randomly-Wired Splitter Networks
IEEE Transactions on Computers - Special issue on fault-tolerant computing
Eigenvalues and expansion of regular graphs
Journal of the ACM (JACM)
A Parallel Algorithm for Reconfiguring a Multibutterfly Network with Faulty Switches
IEEE Transactions on Computers
Large Deviation Bounds for Markov Chains
Combinatorics, Probability and Computing
On the error parameter of dispersers
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
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The expansion properties of regular graphs are investigated. The best previously known expansion of subsets of linear size of explicit k-regular graphs is k/4. This bound is achieved by nonbipartite Ramanujan graphs of degree k=p+1, which have the property that all but the largest eigenvalue have absolute value at most 2 square root p. The expansion coefficient for linear subsets for nonbipartite Ramanujan graphs is improved to 3(k-2)/8. Other results are established, including improved results about random walks on expanders.