We have two new homework assignments for the next couple weeks and I’ll make separate posts for them.

Today we started with Dijkstra’s Algorithm for Single Source Shortest Paths. The reason being that it uses a heap structure to organize nodes that have some minimum distance from the source vertex. The difference is that we need to update (decrement) the value of a vertex in the heap. This is where Fibonacci heaps, which support everything that Binomial heaps do, with the addition of deleting an arbitrary vertex and decrementing the value of an arbitrary vertex.

delete(h, i): O(lg n) (worst case & amortized)

decrement(h, i, D): O(lg n) (worst case) O(1) (amortized)

We didn’t actually cover the structure of Fibonacci heaps, just how we need to modify Binomial heaps to get the bounds we want.

Hopefully, we’ll finish Fibonacci heaps on Wednesday. Don’t forget HW2 is due next lecture as well.

The midterm will be Wednesday, February 22, 2012.

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