Q ok how many steps sufce to be close to uniform top

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 –  card-shuffling –  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: -  top-in-at-random -  riffle-shuffle 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...
View Full Document

Ask a homework question - tutors are online