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Nearly-Linear Time Algorithms for Markov Chains and New Spectral Primitives for Directed Graphs
Presentation on theme: "Nearly-Linear Time Algorithms for Markov Chains and New Spectral Primitives for Directed Graphs"— Presentation transcript:
Nearly-Linear Time Algorithms for Markov Chains and New Spectral Primitives for Directed Graphs - Description
Richard Peng Georgia Tech In collaboration with Michael B Cohen Jon Kelner John Peebles Aaron Sidford Adrian Vladu Anup B Rao Rasmus Kyng Outline Graphs and Lx b G ID: 714179 Download Presentation
. CS6800. Markov Chain :. a process with a finite number of states (or outcomes, or events) in which the probability of being in a particular state at step n + 1 depends only on the state occupied at step n..
The fundamental condition required is that for each pair of states ij the longrun rate at which the chain makes a transition from state to state equals the longrun rate at which the chain makes a transition from state to state ij ji 11 Twosided stat
via . Bases . of . Perfect Matchings. STOC 2013. Marek Cygan, Stefan Kratsch, . Jesper Nederlof. Hamiltonicity (aka Hamiltonian cycle). Held&Karp (‘61. ), Bellman (‘62): . time and space (Dynamic Programming)..
Part 4. The Story so far …. Def:. Markov Chain: collection of states together with a matrix of probabilities called transition matrix (. p. ij. ) where . p. ij. indicates the probability of switching from state S.
We will also see that we can 64257nd by merely solving a set of linear equations 11 Communication classes and irreducibility for Markov chains For a Markov chain with state space consider a pair of states ij We say that is reachable from denoted