A Bit About Dijkstra’s

A Bit of Mathematics

Note that a min-priority queue uses a non-decreasing list of numbers to prioritize vertices. That is, if two vertices have same key, then one of them is chosen at random. In other words, the algorithm depends entirely on the ordering of integers, about which we study in Lattice theory (does words like poset/toset ring a bell?).

Try running the algorithm on the following graph:

Note that it is similar to G we used in sample execution; but w(s,t) = 5.

After Round 1 of Loop execution, which vertex will you choose next? Run it choosing y first and then t. Do we get the correct result?

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