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...C siam review societyfor industrial and applied mathematics vol no pp fastest mixing markov chain onagraph stephen boyd persi diaconis lin xiao abstract we consider a symmetric random walk on connected graph where each edge is la beled with the probability of transition between two adjacent vertices associated has uniform equilibrium distribution rate convergence to this dis tribution i e determined by second largest eigenvalue modulus slem matrix in paper address problem assigning probabilities edges such way as mini mize nding weshowthatthisproblemcanbeformulatedasaconvexoptimizationproblem which can turn be expressed semidenite program sdp allows us easily compute globally for any modest number say using standard numerical methods sdps larger problems solved exploiting various types symmetry structure far subgradient method describe compare those obtained commonly used heuristics maximum degree metropolis hastings algorithm many examples considered substantially faster than these he...