m6 - Lecture C6: Graphs Response to 'Muddiest Part of the...

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Lecture C6: Graphs Response to 'Muddiest Part of the Lecture Cards' (8 respondents) 1) Could the graphs be analogous to Markov chains and then would the weights be analogous to the transitions probabilities ? The Markov chain can be represented as an infinite graph, with probabilities on the transitions instead of weights. 2) Could the shortest path problem also be approached with Markov chains? Maybe for systems with more uncertain weights? Or for systems where future weights are unknowns but estimates exist ? Yes you can. 3) Can you find the shortest path (or least costly) using the adjacent matrix ? Yes, there exists many different kind of algorithms to solve the shortest path problem in graphs. It is common that the algorithms take an NxN adjacency matrix as input and calculates an NxN matrix S, where S i,j is the length of the shortest path from v i to v j , or a special value, e.g., ‘ ’ if there is not path. 4) What is an example of a graph with negative weights ? An interesting question, there are some paths that are undesirable but still have to be
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.

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m6 - Lecture C6: Graphs Response to 'Muddiest Part of the...

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