M. Mihail. Conductance and convergence of expanders. In Proc. of 30th Symposium on Foundations of Computer Science, 1989.  Home/Search   Document Not in Database   Summary   Related Articles

....as Delta t = v t Gamma , and let k Delta t k= P i Delta 2 t (i) Then k Delta t k measures the distance of v t from , so a bound on the rate at which k Delta t k approaches 0 gives a bound on the rate at which v t approaches . Results of Alon [2] Jerrum Sinclair [11] and Mihail [12] show that for t polynomial in n k Delta t k 1=exp(n) The exact polynomial depends on the cutset expansion of the graph and is at most O(n 3 ) The proof in [12] shows this by obtaining an appropriate lower bound on k Delta t k Gamma k Delta t 1 k, the amount by which the discrepancy ....

.... Delta t k approaches 0 gives a bound on the rate at which v t approaches . Results of Alon [2] Jerrum Sinclair [11] and Mihail [12] show that for t polynomial in n k Delta t k 1=exp(n) The exact polynomial depends on the cutset expansion of the graph and is at most O(n 3 ) The proof in [12] shows this by obtaining an appropriate lower bound on k Delta t k Gamma k Delta t 1 k, the amount by which the discrepancy drops in one time step. This bound depends only on k Delta t k and the probability matrix AC 1 and, in particular, does not depend on how the discrepancy k Delta t k ....

M. Mihail. Conductance and convergence of expanders. In Proc. of 30th Symposium on Foundations of Computer Science, 1989.

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