Unformatted text preview: central page and do random walk for sufficiently many steps;
– Restart and repeat sufficiently many times;
– then take PageRank(w) ≈ empirical frequency that random walk ended at w.
• Hope that empirical distribution is good approximation to stationary distribution
for the right choice of “sufficiently many” above…
• or at least for the top components of the stationary distribution, which are the
most important for ranking the top results. Menu
• Random walks on graphs
• Markov Chains
• Examples:
– pagerank
– cardshuffling
– colorings Card Shuffling
Q: Why shuffle the deck?
A: well, to start from a uniformly random permutation of the cards Q2: How many permutations are there?
A: 52! ≈ 2257 ≈ 1077 – how large is that? Q3: Getting a random permutation?
 soln1: dice 1077 faces
 soln2: shuffle ≈ dice Example Shuffles:
 topinatrandom
 riffleshuffle Shuffling as a Markov Chain
Graph:  one node per permutation of the deck. … …  edge (u,v): v is reachable in one move from u (specific to shuffle)
While performing the shuff...
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 Spring '13
 ErikDemaine
 Algorithms, Markov Chains, Markov chain, stationary distribution

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